The incident took place early this morning and under the impact of the collision, the boat suffered damage and sank, they added.
The two fishermen from Pamban were, however, rescued by fellow fishermen and admitted to a government hospital here, police said.
An investigation is underway, they said.
The incident comes days after two fishermen from Pamban were injured after being hit by a stray bullet allegedly fired during a training exercise by the Indian Coast Guard (ICG) personnel in the sea off this island town.