Tributes have been paid to Costa Titch, whose real name was Constantinos Tsobanoglou.
Footage on social media showed him appearing to stumble and fall to the ground during his set before being helped to his feet.
The South African star continued to perform and finished his track a few seconds later before falling for a second time.
The incident reportedly happened in front of fans at the Ultra Music Festival at the Nasrec Expo Centre in Johannesburg on Saturday. He died later in hospital.
In an Instagram post, his family confirmed his death and thanked fans for their support.
"Death has tragically knocked at our door. Robbing us of our beloved son, brother and grandson, Constantinos Tsobanoglou (28), who South Africa had come to love and idolise under his stage name "Costa Titch", they said.
"It is with deep pain that we find ourselves having to acknowledge his passing at this time."
The family added: "We are thankful for the emergency responders and all those present in his last hours on this earth.
"As a family we are faced with a difficult time as we try to make sense of what has befallen us and ask that we be afforded the time and space to gather ourselves.
"The Tsobanoglou family thanks you for the love and support you have given to our son and may you continue to uplift him even in spirit."
UK electronic music group Clean Bandit left a broken heart emoji on the post, while Strictly Come Dancing star Oti Mabuse wrote "Rest in peace" with a tearful emoji.
The Southern African Music Rights Organisation wrote on Twitter: "SAMRO is saddened by the passing of popular rapper Costa Tsobanoglou, better known as Costa Titch.
"Heartfelt condolences to his family, friends and broader music industry."
Costa Titch, whose songs include Big Flexa and Activate, started his career as a backing dancer before making the transition to a rapper.
In February, he announced on Instagram that he had partnered with fellow rapper Akon's record label Konvict Kulture.
In the same month, another South African rapper called AKA, whose real name was Kiernan Jarryd Forbes, was shot dead in Durban. He was 35.
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