Tensions mounted before kick-off as Hungarian fans jeered England players kneeling in support of the fight against racism. The fans also unfurled a banner that showed a kneeling figure crossed out.
The small section of the stadium housing up to 1,000 Hungary supporters then erupted into violence less than five minutes into the game after a group of fans charged up the concourse and steps to clash with police and stewards.
Supporters were seen throwing punches at police before a sizeable group charged through a narrow tunnel into the main concourse area.
Although the disorder settled down inside a minute, riot police wearing body armour and visors then returned to support Wembley's own stewarding team.
London's Metropolitan Police said they had taken action after racial abuse of a steward.
"Shortly after the start of tonight's match at Wembley, officers entered the stand to arrest a spectator for a racially aggravated public order offence following comments made towards a steward.
"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."
The disturbance was followed by the release of a green flare by Hungarian fans after Roland Sallai's penalty opener for the visitors on 24 minutes.
England's Football Association stated: "We are aware of an incident in the away section during tonight's FIFA 2022 World Cup Qualifier at Wembley Stadium. We will be investigating and will report the incident to FIFA."
The rest of the match played out without any other reported incidents.
After the match, Hungary manager Marco Rossi refused to talk about the incidents.
"I don't want to comment on this situation," he said. "It is not my task. Everything I could say could be interpreted in a different way."
Mings said that the players were unfazed at the pre-match jeering and of the anti-kneeling banner.
"We've faced criticism for taking the knee and we have collectively stood passionately together," the England defender said. "That has carried us as a squad. It doesn't change when people hold banners or disagree."
Stones added that he wasn't aware of the incidents but said: "If they were showing those sort of signs to what we believe in as a team, as a nation, I haven't got anything good to say about them as supporters, them as human beings.
"We respect everyone and feel we have an incredible platform to voice our word and that's what we do before the game.
"We stand strong together as a team."
Tuesday's events will lead to more scrutiny of the Hungarian supporters and likely sanctions by FIFA. The country's national football federation has already been fined £158,000 and given a stadium ban by football's governing body after disturbances during September's game between the two teams in Budapest.
In that match, players were hit with objects thrown from the stands and Black players from England's squad were subjected to racist abuse.
The Hungarian Football Federation was also fined €100,000 and hit with a three-game stadium ban by UEFA earlier this year after discriminatory behaviour of fans in Budapest during games staged in the Puskas Arena during Euro 2020.
Wembley's ability to control supporters has also been subject of criticism following extensive trouble at the stadium before and during the Euro 2020 final between England and Italy when hundreds of fans charged barriers to gain entry.
England's FA could also be sanctioned for the flare on the pitch at Tuesday's game as it is their responsibility to ensure safety at home stadiums during qualifying matches.