The victim was taken to Copenhagen's Rigshospital and is not in mortal danger, police said.
“At 10.10pm we received a report that a 23-year-old man was hit by two to three shots in the chest and stomach. When we came out there, the man was found in his apartment,” spokesman Thomas Christensen told news agency Ritzau.
According to witnesses, the shooting occurred right in front of the entrance to the man's apartment building.
Police said that “a man in his 20s of Middle Eastern appearance” was seen running from the scene.
Christensen did not say if the shooting was gang-related but said the victim was “known to police”.