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The fire broke out at Swarna Palace, in the city of Vijayawada in Andhra Pradesh state around 5 am, reports BBC.
However, the firefighter brought the fire under control in half an hour and all surviving patients have been moved to another hospital in the city, officials said.
Prime Minister Narendra Modi said he was "anguished" by the blaze, the second fire at a Covid centre in days.
It is not clear what cause the fire and police are investigating the incident.
The cause is unknown and an investigation has been launched.
Vijayawada Police Commissioner B Srinivasulu told BBC News Telugu that more than 30 people were at the hotel and the death toll was likely to increase.
Prime Minister Narendra Modi said on Twitter that his thoughts were with those affected.
Andhra Pradesh Chief Minister YS Jagan Mohan Reddy has already announced that the victims' relatives will receive compensation of five million rupees (£51,000).
The fire comes after eight patients died at a Covid hospital in Ahmedabad on Thursday after a fire broke out inside its critical care unit.
India has the third-highest number of Covid cases in the world, with more than 2.1 million infections recorded. More than 43,000 have died, according to data from Johns Hopkins University.
On Sunday, the country recorded 64,000 cases, a new single-day record.