The incident happened on October 2 at about 3.30pm outside a convenience store at the junction of Eastmoor Road with Stanley Road.
It happened after the victim, aged 30, and her children were subjected to racial abuse by a man in a car after her daughter dropped a piece of litter outside the store.
Officers would now like to trace the owner of the vehicle pictured in connection with the incident.
Sergeant Zoe Kempa, of Wakefield Neighbourhood Policing Team, said: “We take all hate incidents extremely seriously and racist language will not be tolerated in Wakefield.
“This was an unprovoked verbal attack on a woman with her young child, and I would appeal for anyone with any information on this incident to get in contact with police.”
Anyone with information is asked to contact police on 101, quoting crime reference 13180492276. Information can also be passed anonymously to independent charity Crimestoppers on 0800 555 111.