The suspect, described as caucasian, strolled into a Standard Chartered branch in an expatriate enclave of the city around lunchtime yesterday and handed staff a note with his demands.
Minutes later, he walked out of the branch with SGD 30,000 (USD 22,200) in cash, said a source close to the investigation, who asked not to be named.
A police spokesman confirmed the robbery and said no weapon was used, but gave no details of the note's contents.
Bank robberies are rare in Singapore, whose tough stance against crime and strict ban on private gun ownership have made it one of Asia's safest cities.
The last attempt was in November 2008 when a man disguised himself as a woman threatened tellers with what he called a "bomb" in a paper bag. He was restrained by bank staff and arrested.