All of the victims of the early morning fire were women because the blaze was in the women's wing of the building.
Distraught survivors gathered outside Hospital Number 17, talking of how they awoke in the middle of the night to find smoke everywhere.
They say most of the windows were blocked by metal grills, and doors were locked, but eventually they managed to find a way out.
Authorities say most of the brick building's walls were covered in plastic, which made the fumes particularly noxious, and most victims died of smoke inhalation.
Firefighters say they only received word about 30 minutes after the blaze started.
They believe the fire was set deliberately on a wooden shelf in the hospital's cafeteria, because there were no heaters, wires or any technical reason for the blaze.
Fire inspector Alexander Chupriyan says more people could have been saved, if hospital staff had acted more quickly.
He also says a recent inspection discovered various safety violations at the building, which is at least 40 years old, and hospital staff were told to make changes.
Prosecutors have opened a criminal inquiry that would focus on "intentional destruction" and failure to enact safety measures.
Fatal fires occur frequently in Russia. Most are blamed on aging infrastructure, negligence and poor enforcement of safety rules.