Emergency services were called to reports of an incident at Daldowie Crematorium, off the M74, near Uddingston, at about 12:30.
The two men were taken to Wishaw General Hospital for treatment. There is no update on their condition.
Police said inquiries were ongoing and there was no truth in social media speculation about a firearms incident.
Two men have been taken to hospital following a disturbance at a crematorium in Glasgow.