A woman and a man, both in their 30s, were arrested yesterday on suspicion of child neglect, and have been released on bail.
A number of calls had led detectives to the woman.
The baby, named Joseph by hospital staff, was wrapped in a Hessian bag and left at a doorstep in Lower Wick on 18th July. The baby was only thought to be 24 hours old when he was left.
Since then, Joseph has been cared for by midwives at Worcestershire Royal Hospital, before being passed on to the care of foster parents.
Police believe they have traced the mother of a baby boy who was abandoned on a front doorstep in Worcester in July.
The baby, who was named Joseph by hospital staff, was found outside a house in the Lower Wick area of the city on the early hours of Thursday July 18.
The woman believed to be his mother, and a man in his twenties, were arrested by police yesterday on suspicion of child neglect. They have now been released on bail.
Staff caring for an abandoned newborn baby said he is "a lovely little boy" and is "doing very well".
Patti Paine of Worcestershire Royal Hospital said Joseph, who is believed to have been born yesterday, weighs five and a half pounds and is healthy.
The head of midwifery at a hospital caring for an abandoned baby has urged the boy's mother to seek medical attention.
Patti Paine of Worcestershire Acute Hospitals NHS Trust said:
– Patti Paine
I would like to appeal to Joseph's mother to come forward to us because we believe she may be in need of urgent medical attention.
It's important she's seen by a midwife as soon as possible to get checked over.
A newborn baby boy abandoned on a doorstep in Worcester was found wearing a baby-grow and lying in a hessian shopping bag.
Little baby Joseph - named by the nurses caring for him - was discovered by homeowners alerted by a ring of their doorbell at 4.30am today.
He is now being cared for by children's nurses at Worcestershire Royal Hospital, who say he is healthy and looks as though he was born to term.
Worcestershire Acute Hospitals NHS Trust, which is caring for a baby abandoned this morning in Worcestershire, has made an appeal on Twitter for the newborn's mother to come forward:
Health chiefs are appealing for a mother to come forward after a newborn baby was found abandoned in Worcestershire.
The child was left on a doorstep outside a home in a residential part of Worcester this morning, West Mercia Police said.
Worcestershire Acute Hospitals NHS Trust, which is caring for the child, is making a public appeal for the baby's mother to come forward.
Fifteen fire engines are battling a large blaze at a recycling plant.
Crews were called to a severe blaze at Lawrence Recycling in Stourport Road, Kidderminster, West Mercia Police said.
A force spokeswoman said firefighters expect to be there for "several days" as they try to get the blaze under control.
There has been no need to evacuate local residents but emergency services have advised people to keep all doors and windows closed due to the large amount of smoke in the area.
A number of road closures are also in place.
A sixth man has been arrested in connection with an alleged sexual assault on a child at a day nursery. The man was arrested yesterday by West Mercia Police.
The five men arrested yesterday by police have all been released on bail. They were arrested after the mother of a child who attends the Bright Eyes Nurseries premises reported an incident which allegedly happened last week.
The alleged assault is said to have taken place at one of three premises run by the nursery in Broomsgrove, Redditch and Driotwich, all in Worcestershire. The nurseries have been searched along with three other properties, police said.