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The boy, named Ivan, 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.
Ivan was partially clothed when found, in a city where the daytime temperature is around -17C.
The Russian emergencies ministry said the baby’s mother had also survived and had arrived at the hospital to visit her son.
chelyabinsk regional governor Boris Dubrovsky reportedly said on his Telegram channel that rescuers “heard crying”.
Eight bodies have been found so far in the ruins of the apartment building, amid fears the death toll will rise.
Officials in the Urals region city blamed a gas leak for the blast. Around 36 people are still missing. Media caption
Rescuers searched for survivors after a gas explosion in a Russian apartment block
Authorities earlier announced they had halted their search for survivors until the unstable building could be secured.
“It’s impossible to continue working in such conditions,” emergencies ministry head Yevgeny Zinichev reportedly said, citing a “real threat of part of the building collapsing”.
It will take about 24 hours to secure the building, the BBC’s Sarah Rainsford reported at around 13:00 local time (08:00 GMT) on Tuesday.
Authorities are in a race against time to find survivors, with temperatures expected to fall further overnight.
Russian President Vladimir Putin visited the city to assess the situation
The building was home to 120 people, and 48 flats collapsed in the blast.
“I woke up and felt myself falling,” one witness told Russian television, according to news agency AFP. “The walls were gone. My mother was screaming and my son had been buried.”
Another witness spoke of a “wave of fire” which followed the explosion.
Russia’s Vesti news channel says more than 50 of the block’s residents have been accounted for, including the victims.
The dangerously unstable building must be secured before the rescue can continue
There are more flats on either side of the collapsed block
The blast, at 06:02 local time (01:02 GMT) is thought to have ripped through the first floor, which houses some offices, and the seven storeys above then collapsed. Nearby flats were also damaged.
A criminal investigation has been opened into the disaster.
The city of Magnitogorsk is about 1,695km (1,053 miles) east of Moscow.