Emergency services were called to the scene in Tradeston Street at around 11am on Saturday.
An ambulance attended but the man could not be saved and was pronounced dead a short time later.
An Orange Walk - one of over 30 taking place across Glasgow today - was near the area at the time.
It is not known whether or not the man who died was participating.
His death is not being treated as suspicious.
Kingston Street and Paisley Road in Tradeston were closed due to the incident.
A Police Scotland spokesperson said: "Around 11am this morning, a 68-year-old man became unwell while on Tradeston Street, Glasgow.
“An ambulance attended however sadly the man was pronounced dead a short time later.
"The death is not being treated as suspicious and a report will be sent to the PF."