Visiting Stockport supporters raced onto the field after Kidderminster went 1-0 ahead in the 51st minute, confronting players from both teams. The referee decided to take the players off for safety reasons.
A post on Kidderminster's Twitter feed says "punches thrown at Kiddy players."
The non-league game restarted and Kidderminster won 4-0 to relegate Stockport to the sixth tier.
Crowd trouble marred the FA Cup semifinal between Millwall and Wigan at Wembley Stadium last weekend, when Newcastle fans also clashed with police after a northeast derby loss to Sunderland.