Cyclone Phailin, categorised as "very severe" by weather forecasters, is expected to hit Orissa and Andhra Pradesh states on Saturday evening.
The Meteorological Department has predicted the storm will bring winds up to 220 km/h (136mph).
A deadly super-cyclone in 1999 killed more than 10,000 people in Orissa.
But officials say this time they are better prepared, the BBC's Sanjoy Majumder in Delhi reports.
However, the US Navy's Joint Typhoon Warning Center in Hawaii is forecasting even stronger winds, predicting sustained speeds of up to 269 km/h (167 mph).