Police were responding to 4432 Ruby Road around 6:15 p.m. when the shooting happened.
Investigators say the officers returned fire and that the man retreated back into the home.
Officers took him into custody a short time later.
The man, whose identity was not released, suffered what officers said appeared to be a non-life-threatening wound to the shoulder area.
The officers were not injured.
Police said another person inside the home also sustained a non-life-threatening injury during the incident. It wasn’t clear, however, how that injury happened.
The State Bureau of Investigation will investigate the shooting, a standard procedure in officer-involved shootings.
Fayetteville police said the officers involved would be placed on administrative leave pending the outcome of the investigation.