Wolves had not played West Brom in front of supporters since 2012 and a hostile atmosphere was expected at the Hawthorns.
Tempers flared throughout the game but it boiled over after Matheus Cunha made it 2-0 after 78 minutes, allegedly due to Wolves fans in the home end.
Fights kicked off in the corner of the West Stand and Birmingham Road, while objects were thrown in other areas of the ground.
Fans spilled onto the pitch and the police rushed over to the main incident.
Players remained on the pitch for some time with a handful of Baggies players helping their families sat nearby move away from the violence.
The referee eventually sent both teams into the dressing rooms before they reappeared to finish the game 38 minutes after the violence begun.
Police said six arrests were made and a man is in hospital with head injuries.
West Brom have vowed to work with cops and the FA to find the yobs and they said, “any individual involved in the disorder will be subject to a club ban”.
Wolves added: “Safety and security are of the utmost importance, and the behaviour of those involved is dangerous and inexcusable.
“We will be investigating these serious incidents and appropriate action will be taken.”
West Brom boss Carlos Coberan said: “Unfortunately the game was interrupted by this incident and now we are unable to talk about the atmosphere our fans created, we can’t talk about this aspect.
“Everything before the incident was unbelievable, between both clubs it was very special. Incidents like that we need to avoid.”
Wolves gaffer Gary O’Neil said: “Obviously it’s really disappointing. Anybody that wants to come to watch a football match should feel safe.
“Young children or elderly people could be in that area and we shouldn’t have to discuss incidents like this.
“They shouldn’t happen and I hope everyone’s safe and there are no serious injuries and there are no lasting effects.”