Police said the 24-year-old woman's daughter, who has been nicknamed Mai by welfare workers, has been taken into foster care while police continue to investigate the circumstances under which the child was abandoned at a stranger's house in Auburn on Monday night.

Mai was wrapped in a light green blanket with a picture of an owl embroidered on the front when she was found on the doorstep of a Kirkham Road house.

The homeowner told police that when he answered his doorbell about 9.50pm on Monday, he heard a car speeding away and found the abandoned child.

A bag containing a bottle and formula had also been placed beside her.

"It was a complete surprise," the man said.

"So we called police and they came over and the baby was taken care of, and we just hope that she's okay."

Police said that, following a public appeal to find the child's parents, a 24-year-old woman went to Auburn Police Station on Tuesday afternoon.

Police have confirmed that she is the child's mother.

Detectives questioned her on Tuesday, before she was taken into the custody of the Department of Immigration and Border Protection.

Police have not provided any information about the woman's eligibility to be in Australia, but said investigations were continuing.

They have urged anyone with information to call Crime Stoppers on 1800 333 000 or use the Crime Stoppers online reporting page.