Mahmud Idlibi's dramatic rescue in the flashpoint northern city, a constant target of government air raids, was shown in a video tweeted on Friday by the team that saved him.
The 30-second clip was also posted on YouTube by a group calling itself the Aleppo civil defence, volunteers who operate in rebel-held areas of the city.
The team mistakenly identified the child as a girl but an AFP correspondent met the mother and child on Saturday.
The mother, Umm Mahmud, said her husband and daughter had been killed in the air raid that trapped the baby in the southern Aleppo district of Al-Ansari.
"It was June 18. We were asleep when suddenly I heard a loud explosion. I passed out and woke up in hospital," she said.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"My husband and daughter were killed," said the woman, who has been taken in by her brother in Aleppo's Al-Mashad district.
"We desperately need help," she said, her infant son beside her.
"We have nobody left."
Activists blamed government war planes for the deadly raid.
Mahmud's rescuer, who gave his name as Khaled, told AFP his team had pulled three women and three men from the rubble before realising several hours later that a baby was still trapped.
"The boy was still alive and unhurt. He had spent hours under the rubble. It was a miracle," he said.
In the video the baby is heard crying as its tiny body, completely covered in dust, is carefully extracted.
AFP could not initially verify the authenticity of the video, which was posted nearly a month after the event, apparently because of technical problems.
Daily air strikes by government forces have killed hundreds of people in rebel-held parts of Aleppo, drawing international condemnation.
More than 170,000 people have been killed in the three-year war, one-third of them civilians, according to the Syrian Observatory for Human Rights.
