Emergency services were called to the area at around 7.20am.
The accident happened near the St Vincent Street area of the square.
City centre traffic was delayed while emergency crews responded to the incident.
The man was taken to the city’s Royal Infimary where he was being treated for an arm injury.
A police spokeswoman said: “We received a call at 7.20am that a man had been struck by a vehicle in George Square.
“He suffered an injury to his arm.”