The Welsh Rugby Union has received citing complaints against the players for incidents during the second half of the game from the match citing commissioner Jeff Mark.
The complaint against Morgan was for an alleged breach of Law 10.4 (a) punching or striking an opponent, while Brew was cited for an alleged dangerous tackle.
The result of the hearing will be issued on Thursday.
The Dragons face the Blues at the Cardiff City Stadium on Saturday afternoon as they look to build upon last week's 23-11 victory over the Warriors.
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