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.
Two teenagers in hospital after crashed motorbike sets on fire on Leeds street
Leeds Olympian Nicola Adams and girlfriend Ella Baig reveal baby boy's name as they talk about parenthood
Caught on camera Leeds: West Yorkshire Police need to speak to these people urgently
Met Office storm warning for Leeds - when the stormy weather is due to hit and how long it will last
17 pictures you'll only understand if you're from Leeds
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."