Russian rescuers managed to save the 11-month-old infant from the wreckage, after an explosion in the flats on Monday, in Magnitogorsk.
Chelyabinsk regional governor Boris Dubrovsky reportedly said on his Telegram channel that rescuers “heard crying”, before finding the baby.
Seven bodies have so far been pulled from the building after it collapsed, with fears the number could rise.
The young boy, baby Ivan, was rushed to hospital after being found but has serious frostbite, a head injury and leg fractures, and will be sent for treatment in Moscow.
He is said to be in a “very serious” condition.
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Ivan’s mother also survived the blast and has since been to hospital to see her son, the Russian emergencies ministry said.
“The child was saved because it was in a crib and wrapped warmly,” regional governor Boris Dubrovsky was quoted as saying by the Interfax news agency.
The regional emergency ministry said earlier on Tuesday that 37 residents of the building have still not been accounted for.
The rescue operation was temporarily halted while workers tried to remove or stabilise other sections of the building which were also in danger of collapse.
Hopes of finding survivors were fading because of the harsh cold, with temperatures dropping overnight to around minus 18C (0F).
Seven bodies have so far been recovered and five injured survivors taken to hospital.
Magnitogorsk has a population of 400,000 and is about 870 miles (1,400km) south-east of Moscow.