Police said the incident happened at the corner of Jamaica Street and Argyle Street at about 09:45.
Emergency services attended and the man was taken by ambulance to Glasgow Royal Infirmary. There is currently no information on his condition.
Jamaica Street has been closed while police carry out investigations into the circumstances of the incident.

Initial Environment Agency figures showed £86,000 was spent on a wildlife survey and putting the animals in winter storage at a cost of £24,000.
But the latest figures show the total cost was higher - working out at £2,454 per vole.
The agency said it had a duty to move the legally protected species.
'Feel vibrations'
Previously, the agency said the wildlife survey was not part of the cost of relocating the voles.
But the BBC has since learned the cost of setting up traps along the river banks and checking them over a period of several months was not previously disclosed.
Farmer James Winslade said when annual dredging took place before the agency took over, it had not appeared to affect the vole population.
"They're not stupid, they'll feel the vibration and move on - it's not like they haven't any other habitat to move on to," he said.
"The riverbank adjoins fields so they can move from the riverbanks to the fields."
Money spent on relocating the voles was a small percentage of the £6m spent on dredging five miles (8 km) of the rivers Tone and Parrett, the agency said previously.
The voles spent the winter in an "over-wintering facility" before being moved to Hampshire and Cornwall, according to the figures.
Ecology expert Graeme Skinner said the work required professional, academically-trained people "who hold relevant licences".
"They are undertaking sometimes long, arduous hours in the field to make sure it's up to the standard that is required nowadays," he said.
A man is being treated in hospital after he was struck by a bus in Glasgow city centre.
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A total of £135,000 was spent trapping and moving 55 water voles from the Somerset Levels ahead of dredging work - higher than previously thought.