The baby boy was found wrapped in a blanket by a resident at around 5.30pm. Police say the boy has been taken to hospital and is being cared for by medical staff.
A spokesman for West Midlands Police said: “Mum may be in need of urgent medical attention and she is our absolute priority at the moment.
“We really want to speak to her to make sure she’s OK and would urge her to get in touch.”
Anyone with information is urged to call the police on 101 quoting log 3476 or call the Crimestoppers charity anonymously on 0800 555 111.