Officers responded to a report of a robbery in progress at the Wells Fargo branch at 1145 Broadway at about 11:45 a.m., according to Burlingame police.
Police said a man later identified by investigators as Michael Wayne Brady entered the bank and told the teller that he had a gun.
He demanded large bills and left the building on foot. No one was injured.
The robber's description was broadcast to San Mateo County law enforcement agencies, and Brady was stopped about 30 minutes later by a Daly City police officer in South San Francisco.
The bank teller identified Brady as the robber and he was arrested on suspicion of robbery and commercial burglary, police said.
In a search of Brady's vehicle, police found $5,000 in cash, which was consistent with the amount taken from the bank, police said.