It happened just after 2 p.m. in an area between Ashe Street and Owen Street.
DPD officers were sent to a report of a suspicious person with a weapon in the 2600 block of Owen Street.
When they got there, they said 17-year-old Lafabian Holmes ran. While they chased him, he reached in his waistband and a gunshot was heard.
The teen suffered a gunshot wound to his torso. He was taken to a local hospital where his wound was described as non-life-threatening.
The Durham Police Department said no officer fired a weapon.
When he's released from the hospital, police said Holmes will be charged with carrying a concealed weapon, possession of a handgun by a minor, resisting arrest, and discharging a firearm in the city limits.