Surgeons at Floreasca Hospital in Bucharest used an alcohol-based disinfectant on the 66-year-old woman before carrying out her operation for pancreatic cancer on 22 December.
But they then used an electric scalpel - which, as it came into contact with the alcohol, set the woman's body alight on the operating table.
She suffered burns to 40% of her body and died in hospital a week later.
Police have opened an investigation into the woman's death, local media report.
The victim's family told Romanian media they hadn't been told of "the gravity of the situation" or the details of what had happened - only that it was "an accident".
"We found out some details from the press when they were broadcast on TV stations," they said. "We aren't making accusations, we just want to understand what happened."
Health Minister Victor Costache has promised to investigate the "traumatic" incident.
"We hope to learn from this troubling episode," he said in a statement. "Both myself and the Ministry of Health team that I coordinate will do everything possible to find out the truth."
Deputy minister Horatiu Moldovan added: "The surgeons should have been aware that it is prohibited to use an alcohol-based disinfectant during surgical procedures performed with an electric scalpel."
Romania spends the least on its healthcare system of any EU country, both per resident and as a percentage of its GDP. It has the highest child mortality rates on the continent, along with an underdeveloped hospital infrastructure and a persistent shortage of medical staff.