The company is starting the flights on Aug 1, one of its officials in Dhaka has told bdnews24.com.
He requested anonymity as he was not authorised to speak to the media over the issue yet.
The return flight to Kolkata will start at 7:10pm and end at 8pm.
Bookings can be placed on its website – www.goindigo.in.
The official said they would offer flights at a little over Tk 5,000 and the passengers can collect the tickets at IndiGo office, its sub-agents and airports.
Biman Bangladesh Airlines offers Dhaka-Kolkata one-way flight tickets from Tk 12,500, US-Bangla Tk 10,500. NovoAir Tk 9,999 and Regent Airways Tk 10,000, according to officials of the airlines.
The news of IndiGo flight tickets being available from Tk 5,000 have left passengers excited.
Sajidul Haque, an official of a private firm who visited India recently, said the IndiGo offer will encourage more passengers to travel to India.
Ashraful Islam, official of another firm, said IndiGo would have to maintain standard service despite cheap flights if it wanted to draw passengers.