The attack took place Sunday at Highams Park railway station in Epping Forest, north of London, police said in a release.
The man and his alleged victims -- a black woman with a 2-year-old child in a stroller -- boarded the train at the same station, Walthamstow Central.
Police said the man started taunting the woman with racial slurs during the trip, The Evening Standard reported.
"When the train arrived at Highams Park station, the victim left the train with her pushchair," police said. "She was assaulted by the man, who pulled her hair, dragging her to the ground along with the pushchair. The man then made off from the scene."
The toddler was treated for a broken collarbone. His mother was described as "shocked" but physically uninjured.
Police searched the train station and the area around it but found no sign of the attacker. Investigators have released images captured from security cameras of a man they want to question.
"This was an unspeakable attack on a mother and son, and we are determined to find the man responsible," Police Constable Gerry Hughes said.