The baby's body was discovered by a member of the public in the car park of Morrisons, off the Black Country Route in Bilston, just after 9am on Sunday.
Police officers said on Sunday that they did not know when the baby was born, or how they came to be in the car park. It has not yet been confirmed whether the baby is a boy or a girl.
West Midlands Police had launched an urgent appeal to trace the mother of the baby, or anyone who knows who she is to contact them. The force said they were extremely concerned for the welfare of the woman – but revealed on Sunday evening that she had been located and was receiving appropriate care.
In an updated statement, a spokesman for West Midlands Police said: "We have identified the mother as a result of our earlier appeal and she is now receiving appropriate care.
"We will be speaking to her in due course.
"Thank you to everyone for sharing the appeal."
A spokesman for Morrisons confirmed they were helping police with their inquiries.
A police presence and cordon had been in place on Sunday morning, but had been removed by the afternoon. Photos from the scene this morning showed a number of police cars and ambulances in the car park.
Floral tributes had been left at the scene on Sunday afternoon – with one saying "RIP little one from all at Morrisons Bilston. Fly high angel."
Another added: "RIP buddy."
In an earlier appeal, Detective Inspector Jim Edmonds, from West Midlands Police's public protection unit, said: “This is a truly tragic discovery, and we have 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."
Morrisons in Bilston remained open on Sunday. A spokesman for the supermarket said: "We are helping the police with their inquiries."
Wolverhampton South East MP, Pat McFadden expressed his shock at the tragedy on Sunday afternoon.
He said: "This is a terrible tragedy and the whole community will be shocked and saddened to learn a newborn baby has been found in this way.
"The police have made an appeal for the baby's mother to come forward and I hope that happens as soon as possible."
While a resident who lives near the supermarket, who wished to remain anonymous, said: "I am just so completely shocked by the news. It’s nothing but tragic for everyone involved.
“I don’t think you can ever really imagine this sort of thing happening and it’s hard to find what words to say in a situation like this other than it’s absolutely devastating and so sad.
“It really is heartbreaking and I just hope the mother is found as soon as possible as it sounds like she is in desperate need of help.”
A shopper, who was at Morrisons at the time and does not want to be named, said: "I saw the police, ambulance and private ambulance arrive.
"They went into the blue tent and after a short time after they brought a small black bag out.
"I thought it may have been a body part but later found out it was the little baby."
David Bates said he was shocked to hear what had happened. He said: “It’s just a desperately sad situation.
“A friend of mine told me about it earlier as they had heard about it when they went to the store.
"You don’t expect something like that to happen in such a public car park - I really hope the mother is found soon and gets any help she needs.”
Another anonymous shopper added: “It is just shocking. I had seen some comments on social media this morning that police were outside Morrisons but I couldn’t believe it when I heard a baby had been found.
“My thoughts are with the family.”
Sian Kumar, who lives nearby, said: “We are in a Neighbourhood Watch group and someone had uploaded a photo of an ambulance in the background at the store - that’s all we had seen and someone was asking if they knew what had happened.
“But other than that I hadn’t heard anything, we’d been for a walk around the neighbourhood but hadn’t seen or heard anything.
“It’s really sad to hear that has happened.”
Anyone with information is urged to call West Midlands Police on 1010, quoting log number 842 of April 11. Alternatively, call Crimestoppers anonymously on 0800 555 111.