The match sees Kidderminster looking to gain promotion to League Two, while Stockport are facing relegation.
Supporters from the away end are thought to have attacked opposition players after Harriers took the lead.
An official tweet from the home side read: "Trouble at Aggborough. Fans from Stockport end invade pitch. Punches thrown at Kiddy players. Ref takes players off pitch."
The referee is understood to have restarted the game after taking the players off the pitch.