The man was found in Thorp Street, in the city's Chinese Quarter and near the Hippodrome Theatre, at about 04:10 BST on Monday.
West Midlands Police said the injuries were not life-threatening and the victim was in a stable condition.
Insp Chris Wilkins said the shooting was being treated as "a targeted attack".
An 18-year-old was taken to hospital after being shot in the leg in Birmingham city centre.