Ashulia Police Station Inspector AKM Shamim Hasan said the incident occurred at Primal Food and Drink Limited Factory in Jirabo on Thursday afternoon.
The victims have been identified as Jahangir Alam, 50, Jalal Mia, 45, and Shahidul Islam, 55. They all were from Chandpur.
Inspector Shamim told bdnews24.com that they stayed back for some unknown reason even though the other workers had left the building after work on the roof earlier in the afternoon.
The officials and workers of the factory fled after the incident. Police are yet to find which contractor the victims were working for.
Shamim said legal action would be taken once the families of the victims file a complaint.
EPZ Fire Service official Abdul Hamid Mia said no-one else was found under the debris during the rescue operation.
He believes the roof might have caved in due to the use of low-quality rods, bamboo and cement.