Police arrested 10 people in the Millwall supporters' section of Wembley Stadium on Saturday after violence marred the London club's FA Cup semi-final defeat by Wigan Athletic.
Trouble escalated midway through the second half of Wigan's 2-0 victory with Millwall fans fighting each other and the police.
The Football Association said it "deplored" the "unacceptable" scenes and would seek criminal charges and football banning orders against any offenders.
Millwall, of England's Championship, said they would assist the police and FA with their investigations and that any fans found guilty of violent behaviour would be banned "indefinitely" from the club.
"Ten people have been arrested following sporadic disorder among fans in the Millwall supporters' area at Wembley Stadium," the Metropolitan police said in a statement.
"Investigations into the circumstances of the incidents are ongoing."
The violent scenes were confined to a small number of fans but neverthless overshadowed the game.
Television footage showed several supporters bloodied, police using batons, and a child in tears as the trouble continued.
The FA's general secretary, Alex Horne, said in a statement: "The Metropolitan Police and the FA are this evening investigating scenes of sporadic violence and disorder in the Millwall FC end at today's FA Cup semi-final.
"The FA and Wembley Stadium will work with police and representatives of Millwall FC to review all events.
"We will look to ensure that those involved are identified and we will call for criminal charges and a football banning order to be brought against them.
"The FA deplore the scenes which have taken place and which are unacceptable. Everything will be done to take action against those involved."
A Millwall spokesman told the media that fans involved in the fighting faced a life ban from the club, which has had a reputation for violent disorder among a section of its support dating to the 1930s, when its old ground, The Den, was closed for the first of numerous occasions.
The Millwall chief executive, Andy Ambler, said in a statement on the club's website: "Our position is clear. Anyone associated with our club found guilty of violent behaviour will be banned indefinitely from Millwall matches in addition to any punishment they receive from the authorities.
"Having worked so hard to show the positive side of our club both on and off the field, we cannot allow the actions of a mindless minority to undermine that.
"At this stage we are still in the process of establishing the full details of what happened in a section of the ground during the second half. When we have those facts at our disposal and the police have completed their investigations we may be in a position to comment further."
Millwall manager Kenny Jackett said he had not been aware of the violence as he was concentrating on the match, but that he would make a statement after he had viewed the television pictures.
Wigan manager Roberto Martinez also said he did not see the violence, which took place to the far right of the managers' dugouts.
Martinez added: "It is needless, you don't want to see that in a football game. I have not seen it, normally it is a minority and it just leaves a bad taste."