Fighting broke out in the away end shortly after kick-off after officers attempted to arrest a Hungary fan for allegedly racially abusing a steward.
Another two fans were arrested inside the stadium for the alleged assault of a police officer.
The Metropolitan Police said the trouble was “minor”, though a large group of officers used batons to try to control the clashes with supporters.
There were a further three arrests on the concourse and outside the ground — for affray, drunk and disorderly behaviour and one on suspicion of voyeurism.
A statement from the Met after the game read: “As the officers made the arrest, minor disorder broke out involving other spectators. Order was quickly restored.”
There were early signs of trouble before kick-off when some fans in the away section booed England’s players for taking a knee and held up a sign objecting to the anti-racist gesture.
FIFA have condemned the violence and discrimination and are investigating the trouble, which came in just the second home game since thousands of ticketless fans stormed Wembley for the final of Euro 2020, for which the FA are still being investigated.
There was also trouble elsewhere in Group I, as Poland’s game with Albania in Tirana had to be halted when home fans hurled coins and bottles onto the pitch after the visitors took the lead. Poland went on to win 1-0.
In a statement, FIFA said: “We are analysing reports of last night’s World Cup qualifier matches in order to determine the most appropriate action. FIFA strongly condemn the incidents at England v Hungary and Albania v Poland and our position remains firm and resolute in rejecting any form of violence as well as any form of discrimination or abuse.
“We have a clear zero-tolerance stance against such abhorrent behaviour.”
The FA, who say they were confident enough police and security were on hand for the event, have launched their own investigation and reported the incidents to FIFA, who had a delegation present at Wembley.
Last night’s ugly scenes were the latest in a string of incidents involving Hungary fans. Hungary have been ordered to play home games behind closed doors by both FIFA and UEFA for racist and homophobic abuse in recent months, while they were also fined more than £158,000 by the world governing body in September.
There were racist and homophobic incidents during the games hosted in Budapest at Euro 2020, while England’s players were subjected to racist abuse during their 4-0 win at the Puskas Arena last month.
Tyrone Mings has called on FIFA to ensure the punishment matches the crime after England’s players were booed for taking the knee before the start of the match, which ended in a 1-1 draw.
“We have made it clear why we want to continue taking the knee and we are determined to carry on doing that,” said the Aston Villa defender.
“We’ve faced backlash, criticism before and have stood collectively. That doesn’t change based on banners, people’s views or being opposed to what we stand for. It doesn’t matter to me.
“Every time we speak about racial abuse, the punishments that follow never seem in line with what has happened.
“But I can’t speak too freely unless I know the facts. I sincerely hope if that’s the case the punishment fits.”