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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 blend of African, Cuban and Western influences 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).