Police officer K.N. Bhukan said fire engines restricted the blaze to one floor of the hospital and extinguished it within 30 minutes.
The cause of the fire is being investigated.
The Press Trust of India news agency said the fire started in the intensive care unit of Uday Shivanand Hospital that was treating 33 coronavirus patients.
Some of the patients with fire burns were evacuated to another hospital in Rajkot, a city in western Gujarat state, nearly 1,100 kilometers ( 685 miles) southwest of New Delhi.
In August, a fire killed eight coronavirus patients in a hospital in Ahmedabad, another key city in Gujarat state.
Poor maintenance and lack of proper firefighting equipment often causes deaths in India.