Shabalala passed away at a Pretoria hospital on Tuesday, the band’s manager Xolani Majozi told The Times, a South African news website.
“Yes it’s true. Mr Shabalala passed on this morning,” Majozi said.
“The group is on tour in the US, but they have been informed and are devastated because the group is family,” Majozi added.
Shabalala, who formed the band in 1959 and led it for more than 50 years, retired in 2014 due to ill health but continued to make appearances with the group at events, the news site added.
Ladysmith Black Mambazo has won five Grammys, dedicating their fifth award to the late former President Nelson Mandela.
The band travelled with Mandela to the Norwegian capital, Oslo when he received the Nobel Peace Prize.
The South African government paid tribute to the musician.
“We would like to extend our condolences on the passing of Joseph Shabalala who was the founder of the group Ladysmith Black Mambazo,” the government said in a tweet.
Born in 1941 in the town of Ladysmith in the country’s KwaZulu-Natal region, Shabalala first found fame after he was spotted by the well-known group, the Durban Choir.
But his big break came in 1985 when American musician Paul Simon travelled to South Africa to collaborate with South African artists for his upcoming Graceland album.
Simon collaborated with Shabalala and Ladysmith Black Mambazo and co-composed the now-famous song, Homeless.
The group has also worked with Stevie Wonder and Dolly Parton, among others.