Around 1.2 million people have been evacuated from low-lying areas of Odisha and moved to almost 4,000 shelters, India's National Disaster Response Force said.
Tamannaah Bhatia said, "My prayers with people of Odisha, Andhra Pradesh and West Bengal". Special teams were moving through holiday villages urging tourists to get to safety. But people should not panic unnecessarily. "All precautionary steps are being taken to prevent any loss of life", Kolkata mayor Firhad Hakim told reporters.
Most of the area's thatched-roof houses were destroyed, and there was no electricity.
The cyclone is expected to move towards Chittagong in Bangladesh in a weaker form on Saturday.
Packing sustained winds of 240 kilometers per hour (150 miles per hour), the storm was the equivalent of a Category 4 hurricane on the Saffir-Simpson Hurricane Wind Scale.
At least 200 trains were cancelled across India.
Numerous flights and train services in and out of the state have been cancelled, while schools and government offices are shut. At one Puri hotel visited by AFP all 175 rooms were ordered emptied, causing a wedding party to be cut short.
Dozens of officials were making announcements on hand-held megaphones across the coastal belt asking residents to leave their homes.
Ports were also ordered closed.
Heavy rains lashed the Bangladeshi capital Dhaka and a few coastal districts of the country. "We are all geared up for the challenge", said Sethi. The effect has been catastrophic on the low tension lines that feed the domestic power consumers, an official said.
The National Disaster Response Force dispatched 54 rescue and relief teams of doctors, engineers and deep-sea divers to flood-prone areas along the coast and as far afield as Andaman and Nicobar Islands, a group of islands that comprise a union territory about 1300km east of mainland India in the Bay of Bengal.
The storm is the strongest tropical cyclone to hit India in 20 years.
In a series of tweets, Civil Aviation Minister Suresh Prabhu said Friday that all airlines must immediately respond to the concerns of passengers affected by Cyclone Fani.
"I am not scared", said Loknath, 24, who works in a bookshop in Cottack in Odisha. "Nothing will happen except rain and wind".