'Mai' and mum reunited soon: govt

A baby girl abandoned on a Sydney doorstep will soon be reunited with her mother.

The 18-month-old child, who is being called Mai, is in foster care.

Her 24-year-old mother was taken into custody by the immigration department on Tuesday night after turning herself into Auburn police earlier that day.

The mother and daughter are expected to be back together soon and will live in immigration housing adjacent to Villawood detention centre until their immigration status is resolved.

"Both mother and child are well," a spokeswoman for Immigration Minister Scott Morrison said.

"It would not be appropriate to go into further detail."

Baby Mai was found on the doorstep of an Auburn home on Monday night.

A man, who did not want to be named, answered his doorbell only to find the 18-month-old staring back at him.

Dressed in a black and white top, grey shorts and wrapped snugly in a light green blanket, the child showed signs of being well cared for.

A bag with a bottle and baby formula were also left on the doorstep.

Further comment is being sought from the minister.