The advert has been airing on television since August but drew fresh attention this week after Sabbir's superb batting brought the nation agonisingly close to its first-ever victory over England.
The advert shows Sabbir holed up inside his house drinking a non-alcoholic malt beverage called Oscar before being discovered by the model who is dressed as a policewoman.
The model seductively handcuffs the 24-year-old batsman before he responds that drinking Oscar means "a little privacy is indeed needed".
"BCB has circulated a directive to stop broadcasting of the ad," a BCB official said on condition of anonymity.
"It does not fit with the image of Bangladesh cricket," he told AFP.
The advert has drawn sharp reaction online, mostly from those opposed to 34-year-old model Naila Nayem whose previous promotion of breast cancer screenings was seen by some as sexually suggestive.
BCB requested the malt company to pull the ad. The ad has not aired for the past two days on TV.
Bangladeshi cricketers are feted like rock stars by millions in the Muslim-majority country and are in huge demand to promote everything from noodles to mobile phones.
Sabbir was thrust into the national spotlight after hitting an unbeaten 64 runs in his first Test, which saw Bangladesh almost pull off an upset against England.
There was no immediate comment from Sabbir or Naila.