Part of the 10-story building in Magnitogorsk, Russia, fell following what's believed to be a gas explosion, The Associated Press reported.
At least seven people were killed and dozens remain missing, according to the AP.
The infant was seriously injured in the building collapse and had to be flown to a Moscow hospital for treatment. His mother, who survived the explosion, was able to identify him, state news agency TASS reported.
The recovery efforts have been hampered by the frigid weather, with temperatures falling from 0 degrees Fahrenheit during the day to minus 17 at night.
The explosion happened at about 6 a.m. local time Monday, The New York Times reported, and many residents were sound asleep inside.
Pleas for help could be heard amid the debris after the collapse, according to the Times.