Cyclonic storm Tauktae intensified overnight into a "very severe cyclonic storm", the Indian Meteorological Department (IMD) said. 100 rescue teams have been deployed in Kerala, Karnataka, Tamil Nadu, Gujarat, Maharashtra and Goa.
Cyclone Tauktae is "very likely to intensify further" during the next 12 hours, the weather office said, adding it may cross Gujarat coast between Porbandar and Mahuva in Bhavnagar district on Tuesday morning.
"Ignore rumours, stay calm and don't panic," the National Disaster Management Authority (NDMA) said as it advised people to follow weather updates on radio, TV and newspaper.
Fishermen have been asked not to venture out in the sea.