Police received a call and found the infant just after 11 p.m. by West 44th Street and Seventh Avenue.
The baby was conscious and alert, and taken to Northwell Greenwich Village Hospital to be evaluated.
She did not appear to have been harmed but no one has come forward to claim the child.
Authorities said the baby is estimated to be approximately six months to 1 year old.
Detectives believe they are looking for the abandoned baby's father, who they say frequents the Times Square area. They believe he took the baby during a dispute with his mother.
They are showing a picture of the child to locals and pulling surveillance images from the area, trying to trace his steps.
Their investigation is ongoing, and no arrests have been made.
Under New York State law, it is possible for a parent who is unable or unwilling to care for their child to abandon them -- so long as they take proper measures and ensure the child's safety.
The Abandoned Infant Protection Act allows a parent to abandon a newborn baby up to 30 days of age anonymously and without fear of prosecution, if the baby is abandoned in a safe and secure way.
Under this law, the parent would not be guilty of a crime if the baby is left with an appropriate person or in a safe location like a police precinct, hospital or firehouse. If the baby is over 30 days old, the parent should instead contact an Administration for Children's Services Field Office.