The rider, in her 30s, was seriously injured in the crash on Colley Gate, Halesowen, at the junction with Chapel House Lane and Park Road.
Officers believe a white BMW ran through a red light from Colley Lane into Chapel House Lane and collided with the scooter at around 6.30pm on Tuesday.
The driver of the BMW did not stop.
The woman was treated at hospital for a serious break to her right leg and is now continuing her recovery at home.
Detectives are now appealing for anyone with dash-cam footage to come forward.
Anyone with information should contact police online or on 101 quoting log 3793 of May 4.