The suspect walked into the bank at 914 Carpinteria St. at about 10 a.m. and handed the teller a note demanding money, police Sgt. Eric Beecher said.
The teller turned over an undisclosed amount of cash, and the robber fled the building on foot, heading east on Carpinteria Street and south on Alisos Street, Beecher said.
About 30 minutes later, an officer spotted a man matching the robber's description at Cacique and Voluntario streets, Beecher said.
The suspect ran, and after a chase and a scuffle, he was taken into custody, Beecher said.
He was identified as Joseph Brown, 40, according to Sgt. Dan McGrew, who added that Brown also is suspected in a Dec. 1 robbery at a gas station on Milpas Street.
Brown was booked into Santa Barbara County Jail on two felony countys of robbery, McGrew said.
Most of the money taken in the robbery was recovered during the arrest, Beecher said.