The cat gave birth to the kittens on Wednesday afternoon, said Sajal Deb, the director of Bonno Prani Sheba Foundation (wild animals care foundation) in Sreemangal upazila.
The foundation recovered the fishing cat some months ago from people who caught it in Mirzapur near the Baikkabil wetland.
She mated with a male fishing cat who is also being kept at the centre.
The mother and the kittens were healthy, Sajal Deb said. Arrangements had been made for their safety and health.
The foundation is a recovery and recuperation centre for wild animals in the area, which borders on the evergreen forests in the region, home to several endangered species such as the eastern hoolock gibbon and the capped langur.
The fishing cat is also classified by the IUCN as a vulnerable species.
Having suffered a continuous encroachment on their habitat, wild animals from the region often wander into villages and get attacked and captured by humans.
Sheba Foundation recovers such animals and releases them back into the wild. In July, they rescued a langur that was violently beaten
Foundation staff say the mother and her kittens will soon be released back into the wild, which is the standard practice for the centre.