The incident occurred around 2.00 PM (local time) when around 350 workers were working in the jute mill in Faridpur district, some 100 kms from here, local media reported.
A portion of the tin roof of the mill collapsed during the storm, Jamil Hassan, superintendent of Faridpur police, was quoted as saying.
Four workers, including a woman and a child, were killed in the incident.
The bodies were recovered from the spot while the injured were admitted to Faridpur Medical College Hospital. The condition of 22 of them is said to be critical.