Raheem Sterling and Jude Bellingham were targeted with m chants during the match on September 2 in Budapest, which England won 4-0.
In addition to the stadium ban, FIFA's disciplinary committee imposed a fine of 200,000 Swiss francs (just under £160,000).
A FIFA statement read: "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.
"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."