Atherstone were 4-0 down at the break when a small group of fans, which eventually swelled to around 30, ran onto the pitch and entered the section of the stadium reserved for away supporters.
Fighting broke out in the stands, with one elderly fan reportedly being left bloodied and injured following the attack.
Atherstone substitute Greg Mills, who was warming up on the field during the break, was also seen to be involved in an altercation with a Barrow supporter after being confronted.
The home fans stole a flag from the away end and attempted to burn it as tempers threatened to boil over.
The second half was delayed for 10 minutes before the match finally got back underway, with Barrow going on to secure a 4-0 victory.