Police attended the incident at Saville Green at around 1pm on Saturday (July 2).
The boy was taken to hospital for emergency treatment.
Sadly, he died a short time later.
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West Yorkshire Police has now launched an investigation.
A West Yorkshire Police spokesperson said: "At 1.25pm on Saturday, July 2, police were contacted by the ambulance service who were attending Saville Green in Leeds where a child had fallen from the window of a flat.
"The one-year-old boy was taken to hospital for emergency treatment but was pronounced dead a short time later.
"Enquiries are being carried out to establish the full circumstances.
"The incident is being treated as a sudden unexpected death in childhood and we ask that people consider the family and respect their privacy at what is clearly a very difficult time for them."