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The Tigers drew 0-0 with Arsenal on Saturday and must now find a date for the fifth-round replay in a period where they are already playing 10 games in 35 days.
"It's ridiculous the number of games we have got coming up," said Bruce.
"Why can't we just go to penalties? Why do we have to have a replay?"
Bruce, whose side currently top the Championship, believes it is also unfair on fans, adding: "Supporters have to find the money to support their team."
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Listen: Bruce talks about scrapping replays
The Football Association has reportedly discussed the possibility of playing midweek rounds in the FA Cup, replacing replays with extra-time and penalties, and reducing League Cup semi-finals to one leg.
The aim is to reduce the burden on English teams in European competitions and to keep the national team fresh for summer tournaments.
Manchester City are reportedly "furious" they have to play their FA Cup tie with Chelsea on Sunday, three days before they visit Dynamo Kiev in the Champions League.
And Liverpool boss Jurgen Klopp has said "too many games" harm English football.
"In the past to win a European cup you had to play six or seven games, now it's 17," said Bruce, whose side lost the 2014 FA Cup final to Arsenal.
"We all love the FA Cup and for our club, the final was the biggest day in our lives.
"A footballer can play three games in three days if he wants but you can't play with the energy or intensity that you need to win a Championship game or an FA Cup tie."
Traditionalists have argued to keep replays, predominantly to maintain the possibility of lower-league teams earning big-money fixtures against larger clubs.
And Arsenal boss Arsene Wenger believes the UK's negotiations over its European Union membership are an example of why the FA Cup should remain "a little bit special".
"I like the idea that in England you don't do things like anywhere else. That's why you negotiate in Brussels at the moment as well," said Wenger, whose side face Barcelona in the first leg of their Champions League last-16 tie on Tuesday.
Drawn FA Cup games should go straight to penalties, thus avoiding a time-consuming replay, according to Hull City manager Steve Bruce.