The employee exited the branch near the Cornavin main train station for a break shortly after 1.30pm when an unknown man confronted him with a photo of his family and told him they were being held hostage at their home, Geneva cantonal police said.
Faced with the threat of his family being harmed, the employee went back inside the bank and took a bag containing money, which he gave to the man, police said.
The Geneva prosecutor's office said the cash totalled one million francs, Blick reported online.
The man took the bag and jumped on the back of a scooter driven by an accomplice and the pair headed off in the direction of Lausanne, police said.
The bank employee contacted police immediately afterward.
The family was found safe and sound, police said.
Information about the alleged extortion was transmitted to police in neighbouring France and the canton of Vaud, as well as to federal border guards.
No-one was wounded in the case but several persons were “severely shocked”, police said.
With an investigation under way, under the direction of the Geneva prosecutor’s office, police are not commenting further on the case.