"The BCB has granted him permission to undergo surgery as per the advice of a specialist in Australia," Debashish Chowdhury told reporters.
"Shakib will be out of action for at least six weeks after the operation."
Shakib is visiting Australia to get an expert opinion on the injures that have been troubling him since Bangladesh's home series against West Indies in November last year.
He missed the five-match one-day international series against West Indies because of a stress reaction on his shinbone but made a comeback in the recently held domestic Bangladesh Premier League Twenty20 tournament.
During the BPL, in which he was named player of the tournament, Shakib was diagnosed with exertional compartment syndrome, an exercise-induced problem that causes pain over the front of the shinbone.
"Normally surgery is not always very necessary to recover from this type of injury. But the BCB does not want to risk him aggravating it further as he has some other injuries," said Chowdhury.
"A final decision on when or where the surgery will be conducted will be taken on Monday."
Bangladesh will play two tests, three ODIs and a Twenty20 International in Sri Lanka from March 8-31.