The baby was born at 11.03 am in the railway hospital in Mancheswar, barely five km from the Odisha capital Bhubaneswar, officials said.
As Cyclone Fani raged outside, the doctors maintained their calm and delivered her safely, they said.
The child, born to a 32-year-old railway employee working as a helper at the Coach Repair Workshop, Mancheswar, and the mother are doing fine, said officials of the Bhubaneswar-headquartered East Coast Railways (ECoR).
Packing heavy rain and winds with speeds of up to 175 kmph, Fani slammed into the Odisha coast Friday morning.
"Baby made landfall at 11.03. We are calling her Lady Fani as she was born when the hospital was hit. This was the mother's first baby and both of them are doing fine. The hospital suffered some damage," ECoR spokesperson J P Mishra told PTI
"She was born as the cyclone wreaked havoc and it was raining heavily. The doctors kept their calm and delivered her," Mishra added.
It is not clear if the parents want to name her Fani.
The word 'Fani' means a snake's hood and it was suggested by Bangladesh, said Mritunjay Mohapatra, additional director general of the IMD.
WATCH: Cyclone Fani: Heavy rain, storm lashes Bhubaneswar