Some of England's players were reportedly racially abused by Hungary fans during the team's 4-0 World Cup qualifying win over Hungary.
ITV reporter Gabriel Clarke, who was at the stadium, says he heard monkey chants directed at Raheem Sterling, as well as at substitute Jude Bellingham as he was preparing to come on.
England's players had earlier been loudly booed as they took a knee before kick off, an ongoing gesture to protest racism.
Hungary had been ordered by UEFA, European football's governing body, to play its next three home games behind closed doors after fans' discriminatory behavior at Euro 2020, but this ban wasn't yet implemented as World Cup qualifiers fall under FIFA's jurisdiction.
"Following analysis of the match reports, FIFA has opened disciplinary proceedings concerning the incidents last night at the game Hungary-England," FIFA said in a statement to CNN on Friday.
"Once again, FIFA would like to state that our position remains firm and resolute in rejecting any form of racism and violence as well as any other form of discrimination or abuse.
"We have a very clear zero tolerance stance against such abhorrent behaviours in football."
In a statement, the English Football Association (FA) said it was "extremely disappointing" to hear reports of "discriminatory actions" directed towards some of its players.
"We will be asking FIFA to investigate the matter," the statement read. "We continue to support the players and staff in our collective determination to highlight and tackle discrimination in all its forms."
England and Manchester United defender Harry Maguire wrote on Instagram: "Since last night's match I've spoken to my team mates and seen some of the footage.
"Any discrimination is totally unacceptable and the authorities must look into it. Racism has no place in our game or society."
The Hungarian Football Federation said in a statement to CNN: "The vast majority of the 60,000 fans present in the Puskás Aréna supported the teams in a sporting manner, cheering on the Hungarian national team even when the team was already losing. It is in their defense that the minority of disruptive ticket-holders need to be identified and severely punished.
"Fans entering the field of play, throwing flares and plastic cups are in the process of being identified. The MLSZ has already filed or will file police reports against them and will pass on any financial penalties to the perpetrators through civil litigation. Furthermore, at the end of proceedings, those found guilty can expect a two-year ban from all sporting events.
"The Hungarian Federation and the players, head coach all made an extremely strong communication campaign before the game to call supporters to avoid all kind of racist, xenophobic behaviors during all matches of the national team."
In a later statement to CNN, it added that its "approach to racism on the stands is pretty clear -- it has no room in a football stadium.
"HFF is also consistent on this in club competitions in Hungary. We clearly stated ahead of the game that racism is unacceptable. There are investigations but at this stage we can say anybody who behaved as mentioned will be sanctioned."
England's players also had cups and bottles thrown at them during each of the goal celebrations -- with Declan Rice and Jack Grealish amusingly pretending to drink out of them -- while a flare was thrown onto the pitch as the team celebrated Harry Maguire's goal.
After the game, England forward Marcus Rashford, who is currently out following shoulder surgery, took to social media in support of his teammates.
"My brothers. Every single one of them. Proud of you boys," he tweeted.
UK Prime Minister Boris Johnson, who previously failed to condemn fans who booed England's players while they took the knee, tweeted: "It is completely unacceptable that England players were racially abused in Hungary last night.
"I urge FIFA to take strong action against those responsible to ensure that this kind of disgraceful behavior is eradicated from the game for good."
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