Hungary fans fought with police in the opening minutes of Tuesday’s World Cup qualifier against England at Wembley.
Some of their supporters, totalling almost 1,000, booed as England players took the knee before kick-off.
The Metropolitan Police said “minor disorder” broke out as they arrested a fan for “a racially aggravated public order offence” in relation to comments directed towards a steward.
In a statement, Fifa said it “strongly condemns” the incidents.
Crowd trouble also marred Poland’s World Cup qualifying victory over Albania, with the game suspended for more than 20 minutes after home fans threw objects at the visiting players.
A spokesperson said: “Fifa is currently analysing reports of last night’s Fifa World Cup qualifier matches in order to determine the most appropriate action.
“Fifa strongly condemns the incidents at England v Hungary and Albania v Poland and would like to state that its position remains firm and resolute in rejecting any form of violence as well as any form of discrimination or abuse.
“Fifa has a very clear zero-tolerance stance against such abhorrent behaviour in football.”
On the trouble at Wembley, a Metropolitan Police statement said: “Officers entered the stand to arrest a spectator for a racially aggravated public order offence in relation to comments directed towards a steward.
“As officers made the arrest, minor disorder broke out.”
The game ended 1-1 with John Stones levelling for England after Roland Sallai’s penalty for Hungary.
The Football Association said it would investigate, but England boss Gareth Southgate was unaware of the severity of the incidents at the time.
“I’m only hearing this as I’m doing the interviews,” he told BBC Radio 5 Live after the game. “I was aware of a disturbance. It sounds like it was not acceptable but I haven’t seen the detail.”
Hungary fans – many in the black T-shirts of the country’s ultras – clashed with stewards soon after the game started and police arrived, hitting supporters with batons.
Many then climbed over a barrier in response and hit security personnel – with police driven back into the concourse.
There was trouble too when the sides met in Budapest with Hungary ordered to play two matches behind closed doors by Fifa following the racism English players experienced.
John Murray, commentating for BBC Radio 5 Live, said: “There are about 1,000 Hungary fans in that section. There was black netting over the seats either side to keep it isolated from England supporters.
“We were told before that they were all Hungary fans based in the UK who have taken the tickets. As soon as the match began there were really disturbing scenes.
“There were people in hi-vis jackets and fighting going on in the stands. There were punches being thrown. It was quite aggressive.
“A lot of the supporters involved were wearing black. There was trouble for most of the first half an hour or so and then things seemed to settle down.”
A smoke bomb was also released after Sallai’s penalty gave Hungary a 24th-minute lead.
Fewer than 1,000 tickets were sold to Hungary fans for this game, the reverse fixture of last month’s meeting at Puskas Arena.
Racist abuse was aimed at England players in that qualifier while Southgate’s side were also pelted with objects in the second half and a flare was thrown on the pitch by Hungarian fans. Fifa opened disciplinary proceedings after England’s 4-0 win.
Despite Uefa ordering Hungary to play three home games behind closed doors after their supporters’ discriminatory behaviour at Euro 2020, fans were allowed in for the World Cup tie as it came under Fifa’s jurisdiction.
Football’s world governing body then ordered Hungary to play two matches behind closed doors – one suspended for two years – and fined the Hungarian Football Federation £158,400.
There was also trouble at Wembley when England lost to Italy in the Euro 2020 final on 11 July.
England fans fought with stewards and police as they attempted to break through gates before the match.
Afterwards, riot police could be seen breaking through crowds outside the stadium as people departed.
Beer bottles were thrown amid chants against Italy and the Met Police said there had been 45 arrests at the final, with 19 officers injured “while they confronted volatile crowds”.
Uefa opened disciplinary proceedings against the FA over the events.
