West Midlands Police says a 21-year-old woman and a 36-year-old man are currently in custody.
The baby's body was discovered by a member of the public in the Morrisons car park, off the Black Country Route in Bilston, on Sunday morning.
A post mortem examination will be carried out on the baby, who was not thought to be at full-term.
The mother, who was found after an urgent police appeal, was taken to hospital to receive appropriate care, the force said.
Detective Inspector Tim Draper, from our public protection unit, said: "This was a devastating discovery which I know has shocked and saddened many people.
"I understand this is an emotive event however I’d ask people not to speculate on the circumstances of this tragedy, it’s unhelpful to our investigation which we are working through with dignity and care.”
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."
Wolverhampton South East MP, Pat McFadden expressed his shock at the tragic discovery.
"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," he said.
A resident who lives near the supermarket, and who wished to remain anonymous, added: "“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."