The collision between the Mini Cooper and the VW Bora took place at the junction of Agbrigg Road and Westerman Street in Agbrigg, Wakefield.
It is thought the VW was deliberately driven into the back of the Mini during the incident, which happened at about 4pm on Wednesday.
Wakefield District Police’s PC Jake Scruton said: “Enquiries are ongoing into this incident which is being treated as an offence of criminal damage.
“Both vehicles were in motion during the incident which could well have caused injury and a serious collision.”
Witnesses are asked to contact Wakefield District Police on 101, quoting crime number 13170271188.
Information can also be given anonymously to Crimestoppers on 0800 555111.