Taskin suffered the injury on his left side during a training session on June 23 and missed the third one-day international against India on the following day.
"Usually it takes three weeks to recover. Only in a few exceptional cases can the players return to full fitness early," team physiotherapist Baizidul Islam told AFP.
The injury made Taskin uncertain for the limited-over leg of next month's home series against South Africa.
The Proteas will arrive in Bangladesh next week to play two Twenty20 internationals, three ODIs and two Tests.
"He is very unlikely to play the Twenty20 internationals. We are now trying our best to make him fit before the ODI series," said Baizidul.
The two-match Test series will start in Chittagong on July 21.
Taskin has been an integral part of the Bangladesh team for limited-overs versions since starring for the side in the World Cup in Australia-New Zealand, where he claimed nine wickets for the quarterfinalists.
He took two wickets in the first ODI against India in the just-completed series but went wicketless in the second match.
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