Horrified locals raised the alarm shortly before 7am when officers were called to a report of an incident.
When they arrived in Hoddam Avenue, in Castlemilk, they found the injured man in the road.
He was taken to a nearby hospital. His condition is not known.
A Police Scotland spokeswoman said: "We received a report of an injured man in Hoddam Avenue in Castlemilk, Glasgow at 6.45am today.
"Officers are at the scene and inquiries are currently ongoing."
A section of road at Hoddam Avenue remained cordoned off.