Police said the woman died at the scene from her injuries and a coroner’s report has been filed.
Shakespeare Towers is a 17-storey residential complex located east of the city centre, near St James’s Hospital.
BBC Yorkshire correspondent David Spearl said there was no sign of a police cordon at the scene or evidence of a previous incident.
Since he arrived, a small number of people had come in and out of the apartment, stopping to talk, but no one seemed to know anything about the woman and her baby, he said.
Local councilor Luke Farley said the incident was “extremely tragic” and he was “saddened” to hear the news.
“I would like to express my condolences to the woman’s loved ones,” Farley said.
The Labor MP said the area was full of young families and the high-rise building had been renovated four or five years ago.
He added: “I would also like to reassure residents that police will be present over the next day or so.”
The flats are owned by Leeds City Council, who have been contacted for comment.
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