Police say the alleged assault happened at the traffic lights by Cyril Le Marquand House at about 2 pm.
The woman was driving a silver Ford Fiesta and heading from Union Street towards the Parade when she says another woman got in her car and hit her in the face.
Police believe the two women knew each other and want anyone who saw what happened to get in touch on 612612 or to call Crimestoppers anonymously on 0800 555 111.