Police are appealing for witnesses after the 'fail-to-stop' collision in South Elmsall last week.
Officers said a black car reversed into the 35-year-old mum as she was crossing Valley Road in the town, with her child in a push chair.
The car then left the scene, leaving both the woman and child uninjured but shocked.
The incident, which occurred at around 12.25pm on Wednesday, September 13, was reported to the police last Thursday.
Sergeant David Lockwood, of the South East Neighbourhood Policing Team, said: “Police are investigating this incident in which a car was in collision with a 35-year-old woman and her child while they were crossing the road.
“Fortunately neither were injured and we are keen to locate the driver involved."
Anyone who witnessed the incident or has any information is asked to contact police on 101, quoting log number 0437 of September 13.
Information can also be passed on anonymously to independent charity Crimestoppers on 0800 555 111.