The tragedy occurred a few hours after the 27-year-old scored for Maritzburg United in a 3-3 Premiership thriller against famed Soweto club Orlando Pirates on Sunday.
Cele and another passenger died when the driver lost control of the car, a provincial transport department spokesman said. A third passenger survived.
“His character on and off the field was impeccable,” said Maritzburg chairman Farook Kadodia, referring to 27-year-old midfielder Cele.
Premier Soccer League spokesman Lux September said: “Mondli scored a beautiful goal and it was to be his last celebration.”
Cele was included in the preliminary South Africa squad for the 2015 Africa Cup of Nations in Equatorial Guinea, but did not make the final 23.
His death overshadowed a dramatic weekend of Premiership action highlighted by visiting Pirates coming from three goals behind to hold bottom club Maritzburg.
Cele put United ahead after eight minutes at a packed 10,000-seat Harry Gwala Stadium by side-footing a cut-back past goalkeeper Brighton Mhlongo.
Zimbabwean Evans Rusike, who created the opening goal, scored on 32 minutes and Ugandan Brian Onyango gave United a three-goal advantage soon after.
Thabo Rakhale pulled one back within a minute and captain Thabo Matlaba set up a thrilling second half by scoring a second goal for the Buccaneers early in the second half.
Rattled Maritzburg clung to the lead until 10 minutes from time when Kermit Erasmus equalised, and the visitors looked the likelier winners in frenetic climax of a memorable match.
Maritzburg remain bottom, one point below Pretoria University, while 2015 CAF Confederation Cup runners-up Pirates lie 11th after a disastrous one-win-in-seven start to the season.
At the other end of the table, a seesaw struggle for Premiership supremacy tilted back in favour of record six-time champions Mamelodi Sundowns.
PTI