According to the Goodyear Police Department, officers responded to an apartment near Interstate 10 and Dysart Road just after midnight for reports of a man trying to enter a woman's apartment.
After arriving at the scene, officers found 23-year-old Malaki Cox, who then shoved an officer and ran from the apartment.
During an ensuing foot pursuit, police say Cox displayed a gun and was shot by an officer.
Cox was taken to a hospital and is in stable condition.
No officers were injured and police say Cox and the woman had a prior relationship.