Twenty seven other coronavirus patients being treated at the hospital were rescued.
The cause of the fire is not known yet, but reports say that a short circuit may have led to the fire.
The fire broke out in the ICU of the Uday Shivanand Multi speciality hospital around 3 a.m.
The Gujarat Chief Minister Vijay Rupani ordered a probe into the incident, which has been entrusted to Additional Chief Secretary (ACS) Panchayat and Rural Development Department, A.K. Rakesh.
Expressing grief over the incident, Prime Minister Narendra Modi tweeted: "Extremely pained by the loss of lives due to a hospital fire in Rajkot. My thoughts are with those who lost their loved ones in this unfortunate tragedy. Praying for a quick recovery of the injured. The administration is ensuring all possible assistance to the affected."
The Chief Minister announced a compensation of 4 lakh each to the kin of the victims.
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