The national carrier said one free change of travel date would be permitted for new bookings made till March 31.
"In view of coronavirus situation and travel advisory issued, one free change permitted for pax to postpone any international or domestic bookings on AI network to all existing bookings with travel date till 30th April '20," Air India said in a tweet.
Tickets must be re-issued on or before May 31. In case of re-routing, applicable difference of fare would be charged, it added.
Air India Express, the budget arm of the national carrier, said free date change would be available to fresh bookings made between March 12-31.
It flies to 13 international destinations, mostly in the Gulf region.
"In view of the uncertain travel situation due to COVID-19, free date change will be permitted up to three days prior to the flight departure, for all new bookings effected between March 12, 2020 to March 31, 2020, for travel up to April 30, 2020," Air India Express said in a statement.
Cancellation charges would be levied by both the airlines in case a customer cancels a ticket.
Many countries have imposed travel restrictions, amid the outbreak of coronavirus, which has claimed thousands of lives.
The carrier operates over 660 flights every week to 12 destinations in Gulf countries, including Dubai and Bahrain, besides Singapore. It also has around eight domestic connections per week.
Following the coronavirus outbreak, the airline has reduced the number of its flights to Singapore and has suspended services to Kuwait, an airline official said.
The official also said flights to Doha are likely to be cancelled as the Gulf nation has banned entry of people from India and 13 other countries due to coronavirus scare.
Among other countries, Saudi Arabia has also put in place travel restrictions. Passengers holding Umrah visa and tourist visa have been barred from travelling to Saudi Arabia.
On Sunday, GoAir said it would not charge any fee on cancellation or rescheduling of tickets booked till April 30. This would be applicable for all bookings made between March 8 and April 30, and for the travel period between March 8 and September 30.
The zero cancellation and rebooking fee offer can be availed if done up to 14 days before departure, GoAir had said.
SpiceJet has also decided not to charge change fee on existing bookings made for travel between March 12-31.
It would also be applicable on new bookings for travel between the same period, according to a tweet from the airline.
Fare difference, if any, would be applicable, it added.
AirAsia India has extended free rescheduling of tickets for all travel till March 31 on existing and new bookings. The travel can be rescheduled to any date, as per a tweet.
On Saturday, IndiGo announced waiving of rescheduling charges on tickets booked between March 12 and March 31 for its domestic and international flights.