A man in his 40s was struck by a car on Highgate Road, near the junction of Moseley Road, at around 6.30am on Monday
The blue Renault Clio briefly remained at the scene before being driven off towards Haden Circus.
The car was later recovered in the Highgate area and will be forensically examined as police seek to identify the driver.
The man remains in a critical condition in hospital and police are asking anyone who may have information or dash cam footage to come forward.
A spokesperson for West Midlands Police said: "We know there were other motorists in the area at the time who may have witnessed the collision or seen the heavily damaged Renault Clio make off.
"We're also urging the driver to do the right thing and come and tell us what happened and explain the full circumstances.
"We'll then have a better understanding of what contributed to this collision.
"We can be contacted via Live Chat on our website or investigators directly via firstname.lastname@example.org. Please quote log 418 of 24/01/21. Thank you."