The woman was at South Kensington station when she pushed the pram onto the tube, only for the doors to shut before she could board.
Despite passengers pulling the emergency cord, the train continued to the next station, Gloucester Road.
Transport for London staff called ahead to Gloucester Road, where the baby was taken off the train by a couple and a passenger Malcolm Dyer, 59, before the mother was reunited with her child.
Mr Dyer told the BBC: "She pushed the pram on and all of a sudden the doors shut on to her hands, so she naturally let go and left the baby on there and the train started moving.
"I shouted at someone to pull the alarm, which they did and the train stopped momentarily. The baby was merrily sleeping, unaware of anything that had happened."