The child was discovered by a member of the public at Morrisons on the Black Country Route in Bilston near Wolverhampton on Sunday just after 9am.
It is not yet known when the baby was born or how the infant ended up in the car park.
West Midlands Police said officers were “extremely concerned for the welfare of the baby’s mother, and urgently appealing for her or anyone who knows who she is to come forward.”
Detective Inspector Jim Edmonds, from the force’s public protection unit, said: “This is a truly tragic discovery, and we’ve been treating the scene and the baby with the utmost care and dignity today.
“While we don’t yet know what has happened, what we do know is that there must be a mother out there who is in real need of help − and she is my absolute priority at the moment.
“We have been checking CCTV and speaking to hospitals, but it may be that the mother or someone who knows who she is sees this appeal.
“I really want to speak to her to make sure she’s OK, and to ensure that she can get the help that she urgently needs.”
Anyone with information has been asked to contact police, quoting log 842 of 11 April. Officers can also be reached via live chat at west-midlands.police.uk, or via Crimestoppers anonymously on 0800 555 111.