The Directorate General of Civil Aviation has said that no flight will depart or arrive at Kolkata airport between 9.30 pm tomorrow till 6 pm on May 4 due to cyclone Fani.
The aviation body also said that all flights to and fro Bhubaneswar airport on May 3 stand cancelled.
The 'extremely severe' cyclonic storm is expected to hit the Odisha coast on Friday.
Other states on the eastern coast, such as West Bengal, Andhra Pradesh and Tamil Nadu, are also expected to be affected by the cyclone.
In an advisory, the Directorate General of Civil Aviation (DGCA) said the aforementioned flights are being "cancelled in advance in order to avoid passenger inconvenience and safety of operations".
"Resumption of flights will be with positive clearance from respective air traffic control," the aviation watchdog said in the advisory.
Fani is the most severe cyclonic storm since the super cyclone of 1999 that claimed close to 10,000 lives and left a trail of destruction in vast swathes of Odisha, according to the Joint Typhoon Warning Centre (JWTC).
India Meteorological Department (IMD) sources said it is also the first cyclonic storm of such severity to have formed in April in India's oceanic neighbourhood in 43 years.