Video from the concert shows the artist, who was 66, slumped on the floor as dancers continue to perform, unaware of what is happening.
French broadcaster France 24 confirmed the death, quoting his manager.
On the African music scene since 1969, Papa Wemba won a world following with his soukous rock music.
The Congolese band leader, whose real name was Jules Shungu Webadio, also inspired a cult movement known as the Sapeurs whose members, young men, spend huge amounts of money on designer clothes.
In 2004, he was convicted of people-smuggling in France and spent three months in prison.
The God father fell ill while performing at 05:30 (05:30 GMT) on Sunday, local media report.
Organisers from FEMUA later confirmed Papa Wemba had died during a press conference.
His press spokesman Henry Christmas Mbuta Vokia, told local station Radio Okapi: "Around 5:10, time of Abidjan.
"He sang the first and the second song. While singing the third song, he collapsed.
"I was following the concert live on television. I saw the dancers surround Papa Wemba. I thought it was a scene for the concert.
"But then I see people from the Ivorian Red Cross pop up on stage.
"Suddenly we cut the signal of the Ivorian television. I tried to talk to call the manager of Papa Wemba abroad, Cornelie.
"He told me that Papa Wemba fell during a concert.
"I remember ten minutes later, I was told that he is in intensive care. I call thirty minutes after, Cornelie told me that Papa Wemba passed away."
May His Soul Rest In Peace