The robbery was reported at 9:49 a.m. in the 1000 block of Taraval Street, near 20th Street.
Three suspects came into the bank armed with handguns and wearing black hooded sweatshirts and masks, police spokesman Sgt. Dennis Toomer said.
Two jumped the counter, while the third stayed by the entrance, Toomer said. After the robbery, the suspects fled in a vehicle described as a white sedan.
The FBI is handling the investigation into the robbery, and authorities are looking into whether it is tied to three other recent similar crimes, Toomer said.
On April 19, a Wells Fargo bank was robbed at 725 Irving St. in San Francisco.
Around 11:10 a.m. Monday, a robbery was reported at Metropolitan Bank at 1351 Powell St. in San Francisco and another was reported later that day at the Cathay Bank at 1095 El Camino Real in Millbrae, according to the FBI.
In each of those robberies, the suspects held bank employees and customers against their will, jumped teller counters and took cash. In at least two of the robberies, the trio fled in a vehicle described as a light-colored, older-model sedan similar to a Ford Taurus, FBI officials said.
Witnesses described the suspects as three black men between 20 and 35 years old who had slim to medium builds and wore thick jackets, gloves and other clothing to mask their heads and faces, according to the FBI.
The FBI released surveillance photos taken during the Millbrae and Irving Street robberies and are asking for the public's help in identifying the suspects.
Anyone with information about the cases is asked to call the FBI at (415) 553-7400. Tips can also be sent online to tips.fbi.gov.