"The peak hour of the cyclone is expected from 10 PM Saturday until 4 AM Sunday. All the passengers of the affected domestic flights are being notified and alternate arrangements being offered,"the low-cost carrier said in a statement.
With around 48% share in the domestic air passenger market, IndiGo is the largest airline in India.
The National Crisis Management Committee (NCMC), the country's apex body to handle any emergency, on Saturday reviewed the preparedness to deal with the very severe cyclone 'Bulbul' over the Bay of Bengal.
The cyclone is likely to affect coastal districts of West Bengal and Odisha.
The NCMC meeting, headed by Cabinet Secretary Rajiv Gauba, was informed by the India Meteorological Department that the cyclone has now intensified and is likely to cross the West Bengal coast by Saturday evening.
Heavy to extremely heavy rainfall, accompanied by winds reaching upto 120 Kmph and tidal waves upto one to two metre are expected while the cyclone is expected to make landfall at the West Bengal coast at around 8 pm to 10 pm on Saturday.