Video from the show in Ivory Coast showed him slumped on stage behind a group of dancers, before they rushed to his aid.
His pioneering mix of African, Cuban and also Western sounds became one of Africa’s most popular music styles.
Wemba also toured around the world, and recorded with British artist Peter Gabriel.
“I would put him in the same bracket as Fela Kuti when it comes to influence on African music,” said DJ Edu, BBC 1xtra’s African Music Ambassador.
The musician fell ill in the early hours of Saturday morning. The cause of his death has not been established.
He died before he could be brought to hospital, a spokesman for the Ivosep morgue in Abidjan told Reuters news agency.
Born in 1949, Wemba, whose real name was Shungu Wembadio Pene Kikumba, began his singing career in religious choirs.
He helped modernise Congolese rumba music, with the genre that emerged – soukous – influencing music across Africa.
Together with his bands Zaiko Langa Langa, Isifi and Viva La Musica, he racked up hit after hit, including L’Esclave and Le Voyageur.
He appeared in two feature films, Life Is Beautiful (1987) and Wild Games (1997).
Influence on fashion
Wemba was also a style icon, the driving force behind the cultural movement the Sapeurs, whose young men spend vast amounts on designer clothes.
On his look, Wemba told CNN he in turn was inspired by his parents getting dressed up on Sundays. They were “always well put together, always looking very smart”, he said.
Wemba was performing at a music festival in Ivory Coast before his collapse
Seen here on stage in Paris in 2006, Papa Wemba was a star for more than four decades
Congolese authorities said his death was a “great loss”
In 2004, he was convicted of people-smuggling in France and spent three months in prison.
The conviction related to a racket whereby illegal immigrants were taken to Europe posing as members of his band.
A Belgian court convicted him of the same crime in 2012, handing down a fine of €22,000 (£17,143; $24,690) and suspended prison sentence of 15 months.
He was also once jailed in Zaire (now the Democratic Republic of Congo) for allegedly having an affair with a general’s daughter.
Tributes to ‘icon’
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Media captionFan: “The man was an icon for Congolese music”
Congolese President Joseph Kabila has expressed his condolences, and there are likely to be large events paying homage in the coming days.
Congolese Culture Minister Baudouin Banza Mukalay called his death a “great loss for the country and all of Africa”, Associated Press reported.
“A huge loss”: Kinshasa rapper Youssoupha on Papa Wemba’s death
Kinshasa rapper Youssoupha mourned the band leader in a tweet (in French), saying, “Like my community, I am devastated by the death of Papa Wemba.
“He was the icon of our culture, of our lifestyle. This is a huge loss.”
Source: BBC News