The Ravens - finalists last season - announced the news in a statement on Sunday night.
Bromley were due to play Spennymoor Town in the second round in January.
“The club can confirm that it has been charged by the FA with an alleged breach of competition rules in the FA Trophy,” they said.
“The formal process is ongoing and the club will be attending a personal hearing with The FA week commencing 31st December.
“The club would like to apologise to supporters for the uncertainty this will cause with regards to the next round of the competition and will update supporters with the outcome of the hearing in the New Year.
“The club will not be making any further comment at this time.”
Bromley face Sutton United again on Boxing Day in the National League, before the return game at Hayes Lane on New Year’s Day - a game broadcast live on BT Sport.