Several firefighting units have been dispatched to the factory in the Bayezid Textile area
The Middle East-based group's mouthpiece Amaq News Agency said the target of the attack was security forces, according to terrorism monitoring group, SITE Intelligence.
"The Islamic State's (IS) 'Amaq News Agency reported that the group is responsible for a bombing on Bangladeshi forces in Sylhet," SITE reported.
The police officials were there to assist the assault on the Islamist militants holed up in the hideout.
This is the third incident in Bangladesh in eight days for which the IS claimed credit.
The two others are a blast near the entrance of Dhaka international airport on Friday and a suicide attack on a RAB camp in the same vicinity on Mar 17.