Emergency services were called to the Knightswood area of the city at around 12.35pm on Sunday, STV News reports.
The boy was apparently taken to the Royal Hospital for Children, where he is being treated for serious, but none life-threatening injuries.
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Officers said enquiries are ongoing.
A Police Scotland spokesperson allegedly told STV News: “Around 12.35pm on Sunday, March 9, 2025, we were called to a report of a one-year-old boy injured after falling from a window.
“He was taken to the Royal Hospital for Children in Glasgow for treatment to serious but not life-threatening injuries.
“Enquiries are ongoing to establish the full circumstances.”
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The Glasgow Times has also contacted Police Scotland for comment.