During the first half of Tuesday's game, which ended 1-1, broadcast footage showed Hungarian supporters clashing with stewards and police at Wembley Stadium.
"Shortly after the start of the match, officers entered the stand to arrest a spectator for a racially aggravated public order offence in relation to comments directed towards a steward," the London Metropolitan Police said in a statement to CNN.
"As the officers made the arrest, minor disorder broke out involving other spectators ... Order was quickly restored and there have been no further incidents at this stage."
Footage on social media also showed police retreating out of the stands as they confronted supporters, while fans were also seen holding a banner in protest against England players taking a knee before the match -- an ongoing gesture in football to denounce racism and discrimination.
Meanwhile, Tuesday's World Cup qualifying match between Albania and Poland in Tirana was suspended in the 77th minute after bottles were thrown at Poland's players shortly after the team had scored in the second half.
According to Reuters, a post-match interview with Karol Swiderski, whose goal gave Poland a 1-0 victory, was also cut short as bottles were being thrown at him.
FIFA, football's global governing body, said it is currently analyzing reports of last night's games.
It told CNN in a statement: "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 behavior in football."
Last month, the Hungarian Football Federation was ordered to play its next FIFA-sanctioned home match without supporters and handed a "substantial fine" for racist behavior from fans during a World Cup qualifier against England.
As well as racism, the punishments were also for supporters throwing objects, lighting fireworks and blocking stairways.
Hungary has also been ordered by UEFA, European football's governing body, to play its next three UEFA-sanctioned home games behind closed doors after fans' discriminatory behavior at Euro 2020.
CNN has contacted UEFA in relation to fan behavior at Tuesday's games.