He rose to international prominence in the 1980s with plays that depicted the lives of black people under the racist system of apartheid.
His works “reflected the spirit of resistance” during white minority rule, his family said.
Ngema was best-known for his musical Sarafina!, which was later adapted into a film starring Whoopi Goldberg.
President Cyril Ramaphosa led tributes to the playwright, composer and theatrical director.
Ngema’s “masterfully creative narration of our liberation struggle honoured the humanity of oppressed South Africans” and “exposed the inhumanity” of the apartheid regime, the South African leader said.
He died in a head-on collision on Wednesday evening while returning from a funeral in the town of Lusikisiki in the Eastern Cape province.
More than 700 people have been killed in car accidents in South Africa since the beginning of December.
Born in 1955, Ngema began his career as a backing guitarist before taking to the stage in local theatre productions in the 1970s,.
He went on to co-write the 1981 play Woza Albert! (meaning Rise Up Albert! in Zulu), which imagines the second coming of Jesus Christ during the apartheid era.
The satirical work became the benchmark of South African protest theatre at home and on the stages of London and New York.
He followed up with the musical Asinimali! (Zulu for We don’t have money!), which showed off his exceptional technical abilities as a producer.
And then came his 1987 triumph Sarafina!, set during the Soweto Uprising and carrying to audiences worldwide the revolutionary ardour of South Africa’s youth. It was adapted into a blockbuster movie in 1992.
South African actress Sophie Ndaba said that Ngema would be remembered for generations to come.
“Thank you for inspiring us with your creative work and music,” she said in a her tribute posted on Instagram.
Some of Ngema’s plays after apartheid, which ended in 1994, courted controversy.
He produced Sarafina 2 in 1995 to raise awareness about the scourge of HIV/Aids, which had largely been ignored during apartheid.
It was commissioned by the new government at a cost of 14m rand ($750,000; £590,000) – an amount seen as exorbitant and which triggered an investigation by South Africa’s anti-corruption watchdog, the public protector.
The probe found that the health department’s funding for the play was an “unauthorised expenditure” and its message about HIV/Aids was inadequate.
Ngema also found himself at the centre of controversy in 2002 with his song AmaNdiya (meaning Indians in Zulu), which accused South Africa’s Indian community of racism and exploitation.
It was banned from the airwaves by the Broadcasting Complaints Commission of South Africa, which said that it incited hatred.
Anti-apartheid icon Nelson Mandela, who served as South Africa’s first democratically elected president from 1994-1999, urged Ngema to apologise.
“I think he can do nothing better than to apologise if he has offended anyone with racist lyrics,” Mr Mandela said at the time.
