Siphiwo Ntshebe, 34, was admitted to hospital in Port Elizabeth last week and died on Tuesday, Epic Records said.
He was due to perform his new track Hope at the opening ceremony in Johannesburg on June 11.
Epic boss Nick Raphael said Ntshebe’s death was “a tragedy for all those who believe in the power of music”.
“He had a truly wondrous voice and his music was unique in its melodies and its messages of hope and compassion,” he added.
Epic said Hope was “a soaring track”, featuring “a special message of hope and compassion” written and spoken by Mr Mandela.
The track, and an album of the same name, were due to be released to coincide with the World Cup.
Epic said no final decision had been taken on whether the releases would go ahead but that Ntshebe’s family wanted his music “to be heard by as wide an audience as possible”.
Opening ceremony producer Lebo M said Ntshebe was “a true South Africa World Cup legacy, gone too soon”.
“May his spirit lead us to 11 June 2010. May his soul rest in peace and may Siphiwo’s spirit of hope centre us all,” he added.
The BBC’s Pumza Fihlani in Johannesburg says Ntshebe was relatively unknown in South Africa – his appearance at the World Cup opening ceremony would have introduced him to a much wider audience in his home country.
Ntshebe, who studied at London’s Royal College of Music between 2004 and 2007, had performed throughout Europe.
Mr Mandela had previously praised the tenor as “a young South African with so much talent that has, despite challenges of the past, chosen to work hard at a better future”.