The blaze was reported shortly before 10pm and the cause of the fire is currently unknown.
Three Scottish Fire and Rescue Service crews were deployed to the scene, as well as police officers.
A spokesperson for the SFRS: “We are currently in attendance at a fire at Hairmyres Hospital, East Kilbride.
“We received an alert around 9.45pm and operations control mobilised three appliances. Firefighters remain on the scene.”
The medical facility has capacity for 492 patients and its A&E ward treats patients from different areas of the county.
One local said: “There were sirens going off all over the place with police and firemen rushing about.
“Parts of the hospital are taped off and there’s police standing guard.
“It seems to have happened behind the A&E department, there’s a huge response from the emergency services.
“It’s terrifying that this could happen at a hospital of all places.”