British Transport Police have released CCTV photos of the 'near fatal' incident in an effort to contact the child's parents to ensure the child did not suffer any injuries.
Police said the 'frightening' incident occurred shortly before 7.30pm on Wednesday, July 23.
CCTV images show a man positioning a small child in a pushchair at the bottom of the stairs between two platforms at Goodge Street station.
He briefly leaves the pushchair unattended as he goes to help other family members down the stairs.
A gust of wind in the tunnel catches hold of the buggy and propels it across the platform, onto the tracks - just moments after a train has left the platform.
A woman, thought to be the child's mother, then runs across the platform and jumps down onto the tracks.
Police say she hauled the baby and buggy to safety just seconds before another train pulled into the platform.
Chief Inspector Mark Lawrie said: "This was a frightening incident, not just for the scale of the danger the child was exposed to, but also because the woman then put her own life on the line by going onto the tracks.
"We urgently need to identify the people involved to ensure the child wasn't injured as a result of the fall onto the tracks."
Phil Hufton, Chief Operating Officer for London Underground, said: "London Underground has an excellent and continually improving safety record and such incidents on the Tube are very rare."
If you know the people involved or have any information about the incident, please call the British Transport Police on 0800 40 50 40 or ring Crimestoppers, anonymously, on 0800 555 111, and quote log TSUB/B12 of 11/8/14.