The 36-year-old was on his way to pay in cash at the Royal Bank of Scotland, in Clifton Place, yesterday afternoon when he was attacked.
A spokesman for Police Scotland said the victim drove into a car park at the bank at 2.20pm and, as he made his way to the bank, he was approached by another man who grabbed his bag, which contained "a four figure sum." The robber made off towards Sauchiehall Street.
The victim, who was knocked to the ground, was treated at the Western Infirmary for head and face injuries and later released.
Police Scotland said the suspect was white, of stocky build and between 6 ft and 6 ft 4 ins tall. He was wearing a black woolly hat, blue jacket, shorts and trainers and carrying a rucksack.
Police are checking CCTV from the car park and conducting door-to-door inquiries.
Detective Sergeant Raymond Hunter said: "It's possible the suspect was hanging around outside the bank in the car park and someone may have noticed him.
"I am appealing to anyone who may have been in the car park or the bank and who may have witnessed the incident to get in touch by calling 101 or Crimestoppers on 0800 555 111."