A meeting with Abida Parveen, the warning comes, should be treated like a visit from the pope: as a rare, celestial experience in which you shouldn't ask too many questions or expect much in the way of answers. Parveen doesn't like to talk much. She might not do the interview at all. And yet, 19 minutes of conversation later, it's obvious that the greatest female Sufi singer in history is almost disappointingly blissed out. "My culture – our culture – is rich in spirituality and love," she says, in a densely poetic Urdu. "Sufism is not a switch, the music isn't a show – it's all of life, it is religion. If I want to be recognised for anything, if we should be recognised for anything, it's the journey of the voice. And that voice is God's."

Smoothing herself elegantly on to the sofa of a hotel suite in Manchester, Parveen gives a beatific smile. It would be eerie if it wasn't so soothing; anyone who has watched her on stage knows that this magnificent projection of calm often ends up a wild, sweaty, ecstatic mess. She has admitted to hallucinating while deep in performance and she regularly sends her audiences in Pakistan and India into swaying raptures, swooning and fainting being quite standard reactions. Her first US tour was in 1993 and she has since travelled across the world to perform at sold-out venues.

Björk counts Parveen as one of her greatest musical influences; composer John Tavener – who she performed with last Sunday night at Manchester international festival – said he had a gut-wobbling, primordial experience watching her in rehearsals for their one-off show together. Her own concert last Saturday, where she sang classic qawwalis, ghazals and kafis – all variations on Pakistani folk and classical – was met with yelps and dancing in the aisles of Bridgewater Hall. She credits her father (and God, naturally) for the success.

"I was very attached to my father. Classical Sufi music, for him, came from the soul – I was pulled in by it. We spent hours at the dargahs [Sufi shrines, often built over the graves of saints], singing and reciting at festivals. It was normal in the culture I grew up in."

Parveen, now 59, says she was three years old when she first sang. She was born into a long line of Sufi mystics and singers; her father, Ghulam Haider, founded a devotional music school in Larkana, the Sindhi city in which she was born and, famously, where the Bhutto political dynasty – and its Pakistan People's party – was established. Parveen's talent, decided Haider, outweighed tradition. He trained her throughout childhood, rather than his two sons, to pursue music – "because it was my calling".

She laughs when I ask her about the sexism she might have faced earlier in her Sufi singing career, in such a male-dominated environment: "The concept of being a man or a woman doesn't cross my mind. I'm neither on stage, I'm a vehicle on stage for passion." She is dressed androgynously today as she always is: beige, buttoned-up collar kameez (long tunic) and shalwar (trousers), with a traditional Sindhi print shawl draped over her chest. "I've never felt the need to challenge anyone else – I should be concentrating my energies on challenging myself." To an extent it's true: Parveen's talent transcends any gender expectations back home; she is adored, just as much as her peers Mehdi Hassan and Nusrat Fateh Ali Khan have been.

Parveen's late husband, Sheikh Ghulam Hussain, retired from his job as a producer on Radio Pakistan to mentor and manage her career in the 80s. After he died of a heart attack on an international flight in the early 00s, her daughter Maryam took up the role. There is a sense that Parveen's career has taken a more commercial route as a result. She has performed on Coke Studio, Pakistan's biggest music show, sponsored by the cola company. She joined the judging panel, with Asha Bhosle, of the hugely popular TV talent show Sur Kshetra, which was filmed in Dubai and pitted Indian and Pakistani performers against one another. She even licensed her spiritual ghazals to Bollywood, since her "spiritual brother", Khan, recorded songs for Bollywood films in the 90s.

It's a long way since Parveen's early days, when she would reportedly leave jewellery dropped at her feet on stage, as she didn't want to be remembered for how much she had, rather than what she did. After all, business and Sufism, arguably the purest devotional form of Islam, can hardly make for natural bedfellows?

"The business side. Yes, that has to be for others because this journey, money doesn't come into it. I don't let it enter my mind because it's a pollutant. They tell me to do a show, I do it. Record a CD, I do it. I want this to be peace and love, I go to India so much because of this reason – we used to be one country. I go to Mauritius, Singapore, America, it's my job – I am an ambassador for the heart and will of our Pakistan. This is my destiny."

Unsurprisingly, Parveen laughs and declines to comment on who she voted for in recent elections. She declines to comment, too, on whether Sufism and its music is being used by successive Pakistani governments as a political tool to improve the country's image abroad, rather than there being a genuine state-level interest in preserving and supporting this part of the nation's heritage. After all, the Pakistani Taliban are still bombing and violently attacking Sufi sites and shrines, which are left unprotected and ignored by political leaders. Isn't there a disconnect?

"Pakistan seems disconnected from the outside. But it is built and running on prayers of our Sufi kings, our pirs. Poor people, rich people – we are all God's servants … I'm lucky. My audience is my God."