Jems Robert Koko Bi may be hard to reach by phone, say museum officials. The sculptor is in a forest near Abidjan in his native Ivory Coast, convening a biennale based on his preferred medium – wood. But Koko Bi’s presence in Dakar’s Museum of Black Civilisations is hard to miss. His imposing Cedar Men – four statues of black men made of burnt cedar wood – sits at the heart of Prête-moi Ton Rêve (Lend Me Your Dream), one of the most important exhibitions of contemporary African artists ever to tour the continent.

What his limbless monoliths mean to Africa’s modern art scene – their sombre heads echoing Easter Island and Mount Rushmore – was perhaps best illustrated when guests from various countries spontaneously gathered amid them on the show’s opening night. Silently authoritative, they felt like a natural meeting ground for different cultures, the figures symbolising, in Koko Bi’s words, “the dignity of people who believe in maintaining their native soil and contributing to its development and wellness”.

This is central to curator Yacouba Konaté’s vision as he steers Prête-moi Ton Rêve through the second leg of a two-year tour of Africa. The travelling exhibition takes in seven cities – Casablanca, Dakar, Abidjan, Lagos, Addis Ababa, Cape Town and Marrakech – all of which have exciting new art markets. In a chosen gallery in each city, audiences will see work by 30 of Africa’s biggest artists.

While not all African nations are represented – Kenya and Ethiopia are notable absences – the scope is broad, including South African sculptor Jane Alexander, Malian weaver Abdoulaye Konaté, Algeria’s Zoulikha Bouabdellah pushing the envelope of emergent Arab feminism, Burkina Faso’s Ky Siriki critiquing the economic relationship with Europe, and Chéri Samba injecting the eccentricity of Kinshasa’s streets into paintings filled with irreverent social comment.

Somber monoliths … Jems Robert Koko Bi and his Cedar Men. Photograph: Fouad Maazouz

Africa has produced world-famous names in music, but many of its star artists remain obscure – particularly on the continent itself, where talent leaves to study abroad, sometimes never to return.

“All too often the careers of African artists are built on exhibitions in Paris, Berlin, London and New York … but go by without anybody in Africa actually noticing them,” writes Konaté in his programme notes. “We are haunted by these ghost-like events that create the nagging feeling that Africa’s art scene has been completely ignored.”

Speaking from his home in Ivory Coast, Konaté says he believes “in the power of art [to heal]. But this force is more symbolic than practical. How can one forget that art, especially music, has sometimes been used as instruments of torture in concentration camps and prisons? Artists collaborated with dictators while producing songs that filled hearts with joy. My idea is that artists work for values above money and politics.”

While on the surface the show feels like a celebration unburdened by politics, you don’t need to dig too far to hit hard ground. Its venue in the Senegalese capital invites debate about foreign imperialism both new and old: the museum, which opened last December, was built with Chinese money, and its directors have joined the voices calling for the repatriation of African art from former colonial powers.

The show’s title, Lend Me Your Dream, matches the seeming tranquillity of its curation. But there are monsters lurking in the reverie. You may feel like resting your head on the velvet cushion cradling Siriki’s melted bronze Precious Heads. But from these warped, cracked craniums, griot knowledge is leaking out. Siriki’s anxiety is that oral histories are, generation by generation, ebbing away.

The stories they tell … Precious Heads by Ky Siriki. Photograph: Joshua Surtees

Abdoulaye Konaté’s giant woven masterpiece, Touareg Rouge No 1, may look like a lovingly made blanket to warm you from a Saharan winter. But it is a study of the aesthetic, colours and motifs of Tuareg culture – and potentially a cry for peace. After all, it was Tuareg rebel groups who sparked the Mali conflict that was seized upon by Islamists and has destabilised the Sahel region, displacing hundreds of thousands of people.

Koko Bi’s Two Similar Worlds – a wooden canoe cut in half with a chainsaw and burnt with a blow torch – speaks to the dangers of the exodus of African migrants crossing the Mediterranean. “The young jobless Moroccan man who helped me create it told me he wanted to leave for Europe for a better life,” he says. “I told him Europe isn’t easy and I cut the boat in two and he was so disappointed. I told him to sit in one of the chairs and he felt powerful. I said, ‘That is how you will feel staying in Morocco and looking for a job.’ We live in two similar worlds and neither one is better or worse than the other.”

The impact of European contact with Africa is similarly present in at least two other works. In Siriki’s Africa Faces Its Destiny, young Africans approach white Europeans with begging bowls made from empty tins that once contained rich minerals. But the smiling European bankers have come with two objectives – to dole out wads of cash and simultaneously set up Africa’s debt repayment plan at extortionate rates of interest. They do not appear to notice that one young man who has made it across the sea now lies dead at their feet.

Mansour Ciss Kanakassy’s installation, Le Laboratoire Deberlinisation, explores how African nations ended up in economic and social turmoil thanks to European incursions. Two giant matchboxes feature a logo of the map of Africa, divided and imprisoned by the columns of the Reichstag. On the sandy beach are matchsticks – some burned, some yet to be ignited. It is a metaphor for the Berlin Conference of 1884-85, where Europe’s governments, invited by German chancellor Otto van Bismarck, met to carve up African territory and resources among themselves. It won the Senegalese artist, now based in Berlin, the 2008 Dakar Biennale grand prize.

Catching fire … Le Laboratoire Deberlinisation by Mansour Ciss Kanakassy. Photograph: Joshua Surtees

Art is one way of invigorating African societies that are now emerging economies in their own right, and the Foundation pour le Development de la Culture Contemporain Africaine, who set up the exhibition, hopes to develop connoisseurship among collectors with newfound wealth. Egyptian painter Adel El Siwi, who presented an eye-catching triptych, believes the exhibition is the most important ever seen in Africa. “It is an unprecedented event,” he says, “in that it is fully organised and curated by Africans and does not focus on the African diaspora as a central theme.”

Bouabdellah, meanwhile, sees it as “part of a process of emancipation” from privately foreign-funded projects conceptualised abroad, “demonstrating that south-south cooperation is possible”.

But as well as optimism about the current scene, there is caution, too. “The side effect of these trends is that a great deal of pressure is placed particularly on young artists, to produce for the market, in order to sustain their visibility,” says Alexander. “Which can erode the distinct creative value that brought attention to their work in the first place.”

Nigerian Nnenna Okore’s ceramic and jute pieces, Earthbound and Bride Price, examine the repetitive nature of women’s craft and domestic work culture. “I am aware,” she says, “that I am one of only five women in a group of 30 artists chosen to represent the continent. I feel privileged, but not without recognising that there is still much work to be done in elevating the voice of African female artists.”

Interestingly, two of the five women, Bouabdellah and Alexander, both reference masterworks by men. The former has reinvented Cabanel’s The Birth of Venus in dripping blood-red nail varnish – an antidote to the male-gaze representation of women in western art. “While the French painter shows us a naked body lying prey to desire, I prefer a less virile version, which gives back her status as a woman who is mistress of her own passions,” Bouabdellah explains.

Artist Barthélémy Toguo at work. Photograph: Fouad Maazouz

International visibility is of course vital for African art to thrive. London’s 1:54 art fair has joined Paris’s Pompidou Centre as a regular platform for African artists, and MoMA recently acquired 45 major African artworks donated by Jean Pigozzi to its reopened permanent collection. It is rare, though, to see African art displayed as it is here, without any trace of ethnocentricity or the normally obligatory accompanying texts about the origins of primitivism and early naive work.

Painter Barthélémy Toguo wants more. “We don’t see major European or American galleries coming here,” he says. “I would like the Guggenheim or Pompidou to settle in an African country!”

Looking at the cosmopolitanism and affluence growing out of the dust and bustle of Dakar, this feels like an achievable dream. But does Africa need a Tate gallery? Why should western museums continue to reap the benefits? All over Dakar, small contemporary galleries such as Cécile Fakhoury, Raw and Trames are thriving. On the opening night of local artist Fally Sene Sow’s show at Trames last week, Senegal’s hipsters assembled in a stark industrial space, reminiscent of Hoxton or Williamsburg, with a DJ spinning electro tunes to an excitable, well-dressed crowd.

Where once such an event would prompt stares of astonishment, outside on the busy thoroughfare off Place de l’Independence, taxi drivers in their yellow cabs barely batted an eyelid.

• Prête-moi Ton Rêve is at the Museum of Black Civilisations, Dakar, Senegal, until 28 January. Then travelling to Abidjan, Lagos, Addis Ababa, Cape Town and Marrakech until July.