The girl was stolen by an unidentified man when she was sleeping with her parents, who were contract labourers hailing from Vidarbha region of Maharashtra, at Mumbai's Chhattrapati Shivaji Terminus station on June 10.
The railway police had on Friday released a photograph and CCTV footage to track down the culprit.
The CCTV footage showed a limping man alighting from a train and wandering around the station before spotting the family with the sleeping baby. He then sat besides her and took her away.
The girl's parents used to clean the railway tracks. They were to board a train in the night but missed it, following which they decided to sleep at the station and catch the next train, police said.