The baby fell from the window of a flat in Saville Green, Burmantofts, at around 1pm on Saturday - and later died in hospital.
Police said they were continuing to carry out enquiries.
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Neighbours today told the YEP of their shock in the aftermath of the tragedy.
One neighbour, who did not want to be named, said emergency services descended on the area, which they said was usually quiet, at the weekend.
"There were police and ambulances all over. We didn't know what was going on but then we asked and someone said a little tot had fallen," the neighbour said.
"I knew the mum as they lived directly above me so you would hear the little ones running about. It is just so sad."
The boy is believed to have fallen from a bedroom window in the block of flats in Leeds.
The ten-story tower block is part of a 1959-built estate.
Another neighbour said he knew the little boy.
"If he saw you he would run up and hug you," he said.
"We've lived next door to each other for around 10 years."
He added: "She’s a good mum, and a very nice person. I just can't believe it has happened here. It really is heartbreaking."
A young woman, who lived on the ground floor of the building, said she came home late on Saturday evening to see the flats blocked off by police.
She said: "It's a close community and everyone is just so friendly. It’s tragic. I’ve got a little brother who is four so it’s very close to home.”
Coun Asghar Khan, local councillor for the Burmantofts & Richmond Hill ward, took to social media to express his sadness.
"We were saddened to hear of the sad and tragic death of a baby in our Burmantofts community, our thoughts are very much with the family at this very sad time." he said.
Labour MP for Leeds central, Hilary Benn, said on Twitter: "So sad and awful. All our thoughts are with those grieving for the terrible loss of such a young life."
A Leeds City Council spokesperson said: “We are aware of this incident, and we are working closely with our partners at West Yorkshire Police to establish the full circumstances surrounding this very tragic event.
“We're supporting the family with an urgent transfer into another council property, and we ask that people respect their privacy at what is a very difficult time for them.”
A police cordon around the flat, which had been in place since Saturday, has now been removed.