But as the mercury plunged below zero, mothering Marsha jumped into the box and kept the child warm for several hours with her fur.
Residents in the block of flats discovered the heroic feline protectively curled around the freezing infant and licking his face.
The baby boy was found in clean clothes and with a pack of nappies next to him.
"The baby had only been outside for a few hours and thanks to Masha... he was not damaged by the experience," a hospital spokesman told Central European News.
Nadezhda Makhovikova, who lives in the apartment block, said she ventured into the stairwell after hearing a cat meowing in distress.
"When I went down, I saw it was the baby crying," she told REN TV.
But even after the ordeal was over, Marsha carried on showing her mothering instincts by following paramedics as they took the tiny baby to the ambulance, it was reported.
Vera Ivanina, a paramedic, told REN TV: "She was so worried about where we were taking the baby.
"She ran right behind us, meowing. She was really a rational creature."
The baby boy, believed to be between two to three months old, was taken to hospital where he was declared fit and healthy - despite his hours in the cold.
Marsha has since been treated to a heroes reception back at the block of flats, where residents have spoiled her with food.
The baby is currently being looked after at the hospital, while police have launched a search for the parents.