The Bangladesh Cricket Board (BCB) had approached CSA with the request to play a series in May after their tour to Pakistan, which was scheduled for end of April, was postponed by a court order.
"Unfortunately there are too many practical obstacles that prevent us from accepting this commitment," said CSA Acting CEO Jacques Faul.
"At the moment most of our senior Proteas are spread around the world in England and India (in the IPL) and those who are at home are undergoing rehabilitation from injuries picked up during the past season," he added.
Faul also said that as it is the South African team is scheduled to play a number of series this season.
"We also have to bear in mind that the Proteas' squad has a hectic schedule ahead of it with very important tours to England and Australia with the ICC World Twenty20 in Sri Lanka sandwiched in between," he said.
Faul said he had to agree with the decision of the South African Cricketers' Association (SACA) that the series against Bangladesh could not be accommodated in an already crowded calendar.
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SACA chief executive Tony Irish said that the proposal of Bangladesh series has come in a little too late.
"Unfortunately this request has come through very late in the day by which stage most of the senior players had committed themselves to professional contracts abroad and it would be unfair to ask them to renege on them," said Irish.