The Scottish Fire and Rescue service were alerted to the fire at the disused Stobhill Hospital on Balornock Road, Springburn, at around 6.18pm on Tuesday evening.
At its height, 20 fire appliances were involved in the operation.
Fire crews remained at the scene of the fire overnight, with around 20 firefighters still tackling the blaze this morning.
There are no casualties.
SFRS Area Manager Gordon Pryde said: “The fire has now largely been contained, but this has undoubtedly been a challenging and protracted incident.
“A phenomenal amount of work has been done overnight to bring this fire under control, and to protect surrounding buildings.
“I must praise the response and professionalism of our firefighters – they have been exceptional.
“And I would like to thank our Operations Control firefighters for working effectively with our partners throughout the night and into today.
“There is more work to do, and crews will remain on the scene as they work to extinguish the fire.”