The incident occurred near Baby Supermarket on Friday.
ASI Nurul Islam quoted eyewitnesses to say that the auto caught fire while it was crossing the Baby Supermarket area due to an explosion in its gas cylinder.
The passengers--Abdul Amin, 55, and Abdur Rahman, 22, managed to escape the inferno just in time but still sustained severe burns.
The driver managed to steer the auto out of the main road and hit a tree. This only intensified the fire, which charred the driver before he could be rescued.
The driver's identity is yet to be ascertained.
Meanwhile, the ASI quoted Chittagong Medical College and Hospital doctors as saying that the condition of the injured was serious. They have been severely burnt and are unable to speak.
Amin, who is also the father of the other injured victim, is an Ansar member.