They fell into the shaft - a fall that killed the baby and injured her mother.
The accident happened at 10:20 a.m. at 3415 Neptune Avenue in the Sea Gate section.
The elevator was likely stopped between the 22nd and 23rd floors when the doors opened, officials said.
When the mom pushed the stroller into the elevator, they fell several feet and landed on top of the elevator car.
The elevator then descended to the 15th floor, where it came to a stop.
Someone heard the mother crying out for help, and the rescue effort began.
The mother was being treated at Coney Island Hospital. Family members identified the baby as Areej Ali.
Police believe the elevator was out of service at the time of the incident, but the Buildings Department is checking the maintenance records
They are also looking at the previous repairs to the elevator, and resident complaints that the elevator frequently "jumps" or stops between floors.
Centennial Elevator Company is the elevator repair company.
The Eyewitness News Investigators have learned that the building has had dozens of elevator violations over the last 15 years. We have also learned that the building has a history of residents complaining about broken elevators and other maintenance problems. As recently as September 30, residents reported the elevator was not working.
The high rise was built in 1974, stands 24 stories tall and contains 335 apartments.
Inspectors from the Buildings Department are investigating what happened.
"Our inspectors will remain on scene to conduct a full investigation into this tragic accident. We will be testing all of the elevators in the building to ensure they are operating safely," said a Buildings Department spokesperson.
The building is privately owned and supplies low-income housing. Residents say despite numerous complaints, nothing has been done to make the elevators safe, much less reliable.
"It's terrible but I'm not surprised," said a resident named Diana. "There are a lot of problems with the elevators, people get stuck in them all the time."