The blaze, which has since been contained, forced roughly 150 people to be evacuated from St. George Hospital in St. Petersburg, the country's emergency ministry said. It's not clear how many have been injured.
It started after a ventilator short-circuited, local media reported. All of the patients who died had been on the breathing machines.
Since March, the hospital in Russia's second-biggest city had been re-equipped to treat patients diagnosed with COVID-19.
The blaze occurred as the country was starting to ease certain lockdown restrictions, the television network reported. Construction, farming, and factory workers were beginning to resume certain tasks.
Russia has seen more than 232,243 confirmed coronavirus cases and at least 2,116 deaths from the virus, as of Tuesday, according to data from Johns Hopkins.
Officials believe those numbers significantly undercount the true toll of Russia's outbreak. Treating coronavirus patients has also put a strain on the country's vastly outdated health care infrastructure.
On Monday, the country reported a record daily rise of 11,656 cases. It now has the second most confirmed cases behind the U.S.
St. Petersburg has Russia's third-highest infection rate, with more than 7,700 coronavirus patients and at least 56 virus-related deaths. It has 5,483 hospital beds for patients infected with the virus, according to the BBC.
Police in the city have launched a criminal investigation into the fire.
The Associated Press contributed to this report