"Chris Broad imposed the fines after Graeme Smith's side was ruled to be one over short of its target at the scheduled finish of the Bangladesh innings when time allowances were taken into consideration," said a ICC statement.
"In accordance with the ICC Code of Conduct regulations governing over-rate penalties, players are fined five per cent of their match fees for every over their side fails to bowl in the allotted time, with the captain fined double that amount.
"As such, Smith has been fined 10 per cent of his match fee while his players have each received five per cent fines."
The Bangladesh defeat left South Africa on four points from as many matches and still must face England, West Indies and New Zealand.
They need to win all their remaining matches to be in contention for a place in the semi-finals.
India, Pakistan and the West Indies were the other sides who have been fined for slow over-rates in the tournament.