The deceased were identified as Mohammad Altaf, 40, sukani of FV Sea Heart-1 and Nur Uddin, chief chef of the ship, both hailed from Hatiya upazila of Noakhali district.
Officer-in-Charge of Sadarghat river police station Mohammad Nizam Uddin said the ship had run aground on a shoal in the river during high tide earlier.
Another vessel from the same company was attempting to tow it with a rope but the rope snapped, injuring three workers, he said.
The injured were taken to Ma O Shishu Hospital in Agrabad where two of them succumbed to their injuries on Monday night, he said.
Sub-Inspector Kamal Uddin of the police station said the families of the victims applied for the bodies without autopsy but no decision has been taken yet, reports UNB.
Expressing grief over the deaths, ship owner MA Kader said he is now out of Chattogram.