There is simply no other way of putting it, and nor would earthy British wit have it any other way. A giant bright-blue cock – its feathers proudly upstanding, its coxcomb as stiff as a pennant in the breeze – has been erected in Trafalgar Square, London, and no double entendre is too good for it.

Hahn/Cock, the latest work to fill the square's empty fourth plinth, is by Katharina Fritsch, the German artist (or "sculpture … er, sculptor … er, sculptress", as the city's mayor, Boris Johnson, described her).

Gleefully feminist, the work pokes amiable fun at the vainglorious statues of men (Nelson, George IV, and generals Havelock and Napier) that surround it in this most imperial of British public spaces. "Humour is always a big thing for me," said Fritsch. "It stops things from becoming too severe. I like English humour. It is so often very dark."

The sculpture was unveiled by Johnson, who, despite his claim that "my critical faculties are exhausted by this wonderful sculpture" had plenty to say, not least a thinly veiled jibe at David Cameron's recent efforts to crack down on online pornography. "If you were to Google the sculpture in a few years' time," he said, "search engines would collapse at the behest of the prime minister. Er, quite properly of course." He warmed to the theme later. "You would be forbidden by prime ministerial edict from looking at it," he told journalists. After a meaningful pause, he added: "Quite right too."

Noting the fact that the cockerel is the national emblem of France (a connection registered by Fritsch, she said, only once she had proposed the idea), he added: "I hope French people will not take it as excessive British chauvinism – but for me it stands for the recent British triumph in the Tour de France, which we have won twice in a row … it is a symbol of French sporting pride, brought like a chicken to London. We have mounted this French cock at the heart of our imperial square."

Asked to expand on this particular piece of art criticism by representatives of the French press, Johnson replied: "C'est un jeu d'esprit, c'est une blague" ("It's a witticism, a joke"), but added that he was proud to be the mayor of the sixth-largest French city (home, as it is, to 250,000 French nationals, he said).

Did he feel his manhood crushed by the gentle feminist provocation against male modes of power? "No not at all," he said. "I am happy to channel the power and enthusiasm of that bird; I feel inspired by its regal manner and mood of confidence."

One could almost hear him straining to avoid using the word "cock" (hahn is German for cockerel, and it carries a similar double meaning in Germany). In the last moments before the great black cloths covering the sculpture were loosened, the major invited the crowd to welcome "the big, blue [here came a Pinteresque pause]… bird".

Fritsch said she was intrigued by the prospect of "lively and controversial" reaction from the public. "Art is not made for a few people – it is not an elitist thing." The 57-year-old added that she was delighted by the challenge of a sculpture of hers being positioned so prominently, and the energy that would bring with it.

She said she hoped the work had "many meanings; you can play around with it. It's humorous and also serious". She noted its context not just among "male persons standing on pedestals" – but amid the present-day cocks of the walk. "London is a business centre; there are streets round here like Jermyn Street specialising in men's suits. There's a real male culture around the place."

Fritsch added: "It is a feminist sculpture, since it is I who am doing something active here – I, a woman, am depicting something male. Historically it has always been the other way around. Now we are changing the roles. And a lot of men are enjoying that."

The fourth plinth, as it is known, is in the square's north-west corner. Built in 1841, it was designed to hold an equestrian statue – like its twin, in the northeast corner, that depicts George IV. But funds ran out and it remained empty. In 1998 the first in a series of temporary sculptures for the plinth was commissioned. Works by Rachel Whiteread, Yinka Shonibare, Mark Wallinger and Antony Gormley are among those to have occupied the space since.

Hahn/Cock, which was selected by the Fourth Plinth Commissioning Group (a body that includes artists Grayson Perry and Jeremy Deller), will occupy Trafalgar Square for 18 months.