"The ICC match referee Javagal Srinath of India imposed the fines after Faf du Plessis' side was ruled to be two overs short of its target when time allowances were taken into consideration," said an ICC release.
Under ICC rules players are fined 10% of their match fee for every over their side fails to bowl in the allotted time, with the captain fined double that amount.
"As such, du Plessis was fined 40% of his match fee, while his players received 20% fines."
"If du Plessis is found guilty of one more minor over-rate offence in T20 internationals over the next 12 months, he will receive a one-match suspension as per the provisions of the ICC code of conduct."
South Africa next play the Netherlands in their next group one match in Chittagong on Thursday.
The top two teams from each group will qualify for the semi-finals. The final will be played in Dhaka on April 6.