The incident happened in the Whiterock Drive area of the city shortly after 5am on Tuesday.
A PSNI spokeswoman said the victim was taken to hospital for treatment to his serious stab wounds, which are not believed to be life-threatening.
A man was seen making off in the direction of Whiterock Crescent after the incident.
Detectives in Antrim Road are appealing for information.
They have asked anyone who may have witnessed the stabbing or saw the man making off from the scene to contact them.