Video footage has emerged of Hungary fans chasing police officers out of their compound during their match with England on Tuesday night.
The footage showed a small group of police officers, armed only with batons, being forced back by a mob of around 1,000 travelling fans.
The violence broke out when police moved in to try and arrest one of the Hungary fans for making a racist comment to a steward.
Oliver Dowden, co-chairman of the Conservative Party and a former Culture Secretary said the events at Wembley were "deeply disturbing".
Oliver Dowden, co-chairman of the Conservative Party and a former Culture Secretary said the events at Wembley were "deeply disturbing".
Dowden told ITV: "I know that the FA will be investigating this fully and engaging with FIFA as well. There's clearly still an underlying problem with racism in football."
England players Raheem Sterling and Jude Bellingham were subjected to racist chants in Budapest last month when England beat Hungary 4-0.
Hungary were ordered to play two home games behind closed doors following the incidents at the Puskas Arena.
FIFA said it would be investigating the violence at Wembley and also disturbances in Tirana where play was held up for 20 minutes as Albanians fans threw missiles at Polish players during Poland's 1-0 win.
FIFA said: "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."
England defender Tyrone Mings said: "Every time we speak on racial abuse the punishments that follow never seem in line with what has happened. I sincerely hope that if that is the case, the punishments fall in line with what happened this time."