A 4-0 thrashing by Gareth Southgate's side in early September was overshadowed by reports of racial abuse directed at Raheem Sterling and Jude Bellingham by the home fans.
Objects were seen flying in Sterling's direction after his opener, with alleged monkey chants also coming from inside Puskas Arena, as England coasted to victory.
FIFA's Disciplinary Committee has also issued the Hungarian Football Federation (MLSZ) a fine of 200,000 Swiss francs ($299.500), with a qualifier against Albania on 10 October (AEST) the game that will be played without spectators in Budapest.
A suspended penalty of a second game was imposed by the world's governing body for a probationary period of two years.
"After analysing and taking into consideration all the circumstances of the case, specifically the seriousness of the incidents (racist words and actions, throwing of objects, lighting of fireworks, blocked stairways), the Committee decided that the MLSZ would play its next two home matches in FIFA competitions without spectators, the second match being suspended for a probationary period of two years," a FIFA statement released on Wednesday (AEST) read.
"FIFA's position remains firm and resolute in rejecting any form of racism and violence as well as any other form of discrimination or abuse. FIFA takes a clear zero tolerance stance against such abhorrent behaviour in football."
This is not the first time Hungary has been sanctioned by football's governing bodies. In July, Hungary was ordered to play three UEFA home competition matches without supporters after incidents of racism and homophobia at UEFA Euro 2020.
The ban applies only to UEFA competitions and so will not come into effect until the next edition of the UEFA Nations League, which will be held between June and September 2022.