McLaren, the ex-partner of designer Vivienne Westwood, was diagnosed with a rare form of cancer last October.
He set up a clothes shop and label with Westwood on London’s King’s Road in the 1970s and was later a businessman and performer in his own right.
The couple had a son, Joseph Corre, the co-founder of lingerie shop Agent Provocateur.
When we were young and I fell in love with Malcolm, I thought he was beautiful and I still do
His agent told the BBC that McLaren passed away on Thursday morning.
Spokesman Les Malloy said the artist’s family was “devastated” and “in shock” after his condition suddenly deteriorated, adding: “He had been doing very well, it’s a sad day.”
McLaren’s son said funeral arrangements had not yet been made but his father wanted to be buried in Highgate Cemetery, north London.
Paying tribute to his father, he said McLaren was the “original punk rocker” who had “revolutionised the world”.
“He’s somebody I’m incredibly proud of. He’s a real beacon of man for people to look up to,” he said.
Young Kim, 38, McLaren’s partner of 12 years, described him as the “ultimate postmodern artist”. McLaren had been diagnosed with mesothelioma – a rare form of cancer – last October, she said.
Westwood paid tribute to her former partner and said Joe and her other son Ben were with McLaren when he died.
“When we were young and I fell in love with Malcolm, I thought he was beautiful and I still do.
“I thought he is a very charismatic, special and talented person. The thought of him dead is really something very sad.”
Former Sex Pistol John Lydon issued a tribute signed Johnny Rotten – the name he used in the band – which said: “Above all else [Malcolm] was an entertainer and I will miss him, and so should you.”
McLaren also managed a number of other bands, including the New York Dolls and Bow Wow Wow before producing his own records including the much-sampled track Double Dutch from the 1983 album Duck Rock.
McLaren emerged from art school in the 1960s and, with Westwood, set up Let It Rock – a fashion store specialising in rubber and leather fetish gear.
It was later, infamously, renamed “Sex” and he and Westwood defined punk fashion.
McLaren was involved in putting the Sex Pistols together in 1975 and under his management the band courted controversy.
After their debut single Anarchy in the UK was released in December 1976, the band became a household name when they swore on Bill Grundy’s TV show.
Their concerts faced difficulties with promoters and authorities and they were fired by both EMI and A&M records.
In 1977, their single God Save the Queen was banned by the BBC. The band broke up at the end of a US tour in January 1978 and McLaren then created his disputed film version of the Sex Pistols’ story, the Great Rock ‘n’ Roll Swindle.
But there was a falling out with the band members and he later lost a court case over royalties.
After retreating from the music scene, McLaren dabbled in politics and at one point toyed with the idea of entering the race to be mayor of London.
In 2007, he pulled out of an appearance on the reality show I’m A Celebrity… Get Me Out of Here, after changing his mind about the show.
Between December last year and this January, the Baltic Centre for Contemporary Art in Gateshead hosted an exhibition by McLaren of “musical paintings” on the issue of sex.
Music journalist Jon Savage said: “Without Malcolm McLaren there would not have been any British punk.
“He’s one of the rare individuals who had a huge impact on the cultural and social life of this nation.”
Mr Savage, who wrote a definitive history of the Sex Pistols and punk, England’s Dreaming, said McLaren was a “complex” and “contradictory” character who had influenced British culture in many ways.
“He could be very charming, he could be very cruel, but he mattered and he put something together that was extraordinary.
“What he did with fashion and music was extraordinary. He was a revolutionary.”
Creation Records founder Alan McGee described his late friend as a “visionary”.
The BBC’s creative director Alan Yentob said he was saddened by the news but McLaren was “clearly suffering” during his last months.
They became friends after meeting in the 1980s.
He said McLaren was a “significant figure” in British music: “Without Malcolm, despite what people say, the punk era would never have been the kind of focus that it did become.
“Malcolm loved the idea of it and it was he, who, in a way, sold the idea to the public and understood what it meant.”
He said: “Malcolm was a man of ideas really – he was fascinated by ideas. He was always thinking about the next one. He was always ready to say something provocative.
“I think he famously said that his grandmother told him you needed to be a bad boy to survive – it was good to be bad. He wanted to shock and surprise you.”
Sylvain Sylvain, founder member of New York Dolls, said McLaren “really was a piece of sugar” who would be remembered as a “cool guy”.