The girl, who is under the age of one, has been taken into care by the Department of Social Development as the investigation continues, said Saint John Police Force Sgt. Jay Henderson.
The incident occurred on Monday night on Paddock Street, in the city's uptown, said Henderson.
A neighbour heard a baby crying at about 6 p.m. and went outside to find the infant unattended in a carrier on the sidewalk, he said.
When no parent or guardian could be found, the neighbour called police.
The infant was clothed and had a blanket around her, said Henderson. But temperatures had plummeted to about -16 Celsius, he said.
"As a result of this, obviously it's a serious issue. That's why we have the Department of Social Development involved. Any time that there's an issue with any child welfare or health concerns, we always involve the department."
It's unclear how long the infant was outside or why she was left alone, said Henderson.
The woman was arrested and later released on a promise to appear in provincial court on March 19.
Henderson could not confirm whether the woman is the infant's mother or whether she has any other children.