"Unfortunately there are too many practical obstacles that prevent us from accepting this commitment," CSA chief executive Jacques Faul said.
"At the moment most of our senior Proteas are spread around the world ... and those who are at home are undergoing rehabilitation from injuries picked up during the past season.
"We also have to bear in mind that the Proteas squad has a hectic schedule ahead." South Africa tours England and Australia either side of the World Twenty20 in Sri Lanka in September.
The South African Cricketers' Association said the request from Bangladesh came 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," SACA chief executive Tony Irish said.
"The Proteas team management and players have also put their plans in place in the build-up to their tour of England and it would be impossible to change them at this stage." South Africa's tour to England starts in July.
The Bangladesh Cricket Board has been trying to line up international matches since being forced last week to postpone a two-match tour of Pakistan when the country's High Court ordered it be delayed because of security concerns.
