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.
Police said on Sunday afternoon that they did not know when the baby was born or how the body ended up in the car park.
Following a public appeal for help, the infant’s mother was traced by officers on Sunday evening.
“She is now receiving appropriate care,” a spokesperson for West Midlands Police said. “We will be speaking to her in due course. Thank you to everyone for sharing the appeal.”
Officers had earlier said they were “extremely concerned” for the mother’s welfare.
Detective Inspector Jim Edmonds, from the force’s public protection unit, said in a statement: “This is a truly tragic discovery, and we’ve been treating the scene and the baby with the utmost care and dignity today.”
He said officers had been checking CCTV and speaking to hospitals in an attempt to trace the mother to “make sure she’s OK, and to ensure that she can get the help that she urgently needs.”
Anyone with information was 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.