CSA chief executive Jacques Faul says there are too many “practical obstacles” to the Bangladesh series, including a hectic schedule for the Proteas.
South Africa tours England and Australia either side of the World Twenty20 in Sri Lanka in September.
South African Cricketers' Association chief executive Tony Irish says the request from Bangladesh came “very late in the day” and South Africa rather wanted to make sure its players were fresh for the three-test series in England, which starts in July.
Bangladesh last week had to postpone a two-match tour of Pakistan after the country's High Court ordered it be delayed because of security concerns.