The man entered the branch on a large main road in the Dornbusch area north of the city centre at around 9.40 am.
He said that he had a bomb and was prepared to blow himself up, the Frankfurter Allgemeine Zeitung (FAZ) reported.
A police spokesman told the Frankfurter Rundschau that the robber had placed a package on the bank counter that staff believed to be a bomb.
After the cashiers handed over an unknown amount of cash, the robber fled – only to be caught around an hour later by police at the city's convention grounds (Messegelände).
Law enforcement tweeted that they had got their man at 10.44 am, adding that no-one was hurt.
Police had launched a huge search involving large numbers of officers and a helicopter.
A bomb dog sent to the bank found no trace of explosives, police tweeted.
Im #Dornbusch kam es zu Bankraub-wir fahnden nach Täter. Es musste gesperrt&Hubschrauber eingesetzt werden.In der Bank KEIN Sprengstoff *fm— Polizei Frankfurt (@Polizei_Ffm) January 25, 2016
That allowed the lifting of a blockade on the streets and U-Bahn stations on the U1, U2, U3 and U8 lines around the branch - although there were continuing delays on some lines.