Bellingham lashed out at Zwayer in an interview with Norwegian broadcaster Viaplay Fotball after the game, bringing up the official's involvement in a 2005 match-fixing scandal.
'You give a referee that has match-fixed before, the biggest game in Germany what do you expect?' said the England midfielder.
Jude Bellingham hit out at referee Felix Zwayer after Borussia Dortmund's loss to Bayern Munich
Bellingham appeared to be referring to Zwayer being banned for six months for accepting a €300 (£256) bribe from fellow referee Robert Hoyzer. He returned to refereeing after the German league were satisfied he had served his punishment and undergone a process of rehabilitation.
And according to German newspaper Bild, Bellingham could be about to be hit with a suspension for his comments.
Bild has reported that referee's observer Marco Haase has filed a charge against Bellingham and former German referee Manuel Grafe, who had criticised Zwayer in the past for his involvement in the 2005 scandal.
Haase believes Grafe's past statements about Zwayer had an influence on Bellingham.
Grafe had previously said: 'Anyone who has ever accepted