The 21-year-old woman and 36-year-old man were arrested after the baby's body was discovered by a member of the public in the car park of Bilston Morrisons on Sunday morning.
They were arrested on Monday but have now been bailed, West Midlands Police said.
The force has not confirmed what crimes the pair were arrested on suspicion of committing.
Meanwhile a post mortem examination is due to be carried out on the baby, who was not thought to be at full-term at the time of death.
The mother was tracked down on Sunday afternoon following an urgent police appeal in response to the baby being found in the car park next to the Black country Route.
She was taken to hospital to receive "appropriate care", West Midlands Police said.
Flowers were left at the scene on Sunday afternoon, with one saying "RIP little one from all at Morrisons Bilston. Fly high angel."