Two police horses and two police dogs were also injured during the disorder outside Villa Park, which saw missiles and flares thrown.
Police described the scenes as “disgusting and highly dangerous”, and UEFA on Friday morning said they strongly condemned the “unacceptable violence”.
The governing body were gathering official reports from the game before deciding on potential next steps. Last night’s match, which Villa won 2-1, went ahead, but Legia fans were not allowed into the away end.
A statement from West Midlands Police read: “We were faced with disgusting and highly dangerous scenes as trouble flared ahead of the fixture.
“We had a significant policing presence because of safety concerns. This stemmed from visiting fans being involved in previous match day disorder.
“This disorder is believed to have sparked when tickets were not distributed by Legia to supporters outside the ground, as had been anticipated.
“Officers faced 90 minutes of sustained violence and, during the disorder, four officers were injured, along with two police horses and two police dogs. Thankfully, their injuries are not believed to be serious.
“All of those arrested are away fans, and we’ll be working hard to charge and remand those suspects where we can today. We will further review all available footage to identify perpetrators.”
Of those arrested, four were for possession of offensive weapons and four for assaulting emergency workers.
Villa have lodged an official complaint with UEFA over the incident. Chris Heck, the club's president of business operations, said: "The lack of cooperation and prevarication from Legia Warsaw officials prior to the match was entirely unacceptable and deeply disappointing."
Legia’s ticket allocation had been reduced due to fears of trouble. The club was fined €15,000 (£12,915) last month and banned from selling tickets for its game at Bosnian side Zrinjski Mostar after trouble at the match against Dutch club AZ Alkmaar.
Villa said they let no away fans into the ground on police advice. The club had previously raised concerns with UEFA about the prospect of ticketless fans trying to get into the ground.
UEFA, who can hand out punishments for incidents inside the ground and the nearby vicinity, said in a statement: “We strongly condemn the unacceptable violence which occurred. We are in the process of gathering all official reports before deciding on potential next steps.”