A late Yannick Sagbo strike salvaged a 1-1 draw for Hull against their Championship rivals on Monday after Argentine Leonardo Ulloa had opened the scoring on the half-hour.
The top-flight club will now host the replay on Monday, 48 hours after they travel to second from bottom Cardiff, with the rules of European soccer's governing body UEFA preventing the game being played on the same night as next week's Champions League fixtures.
"I find that ridiculous," Bruce was quoted as saying by Sky Sports television. "Surely we could play on the same night as the Champions League.
"It is quite a bizarre one, isn't it? For (UEFA) to say to the FA that we can't play the same night as they are playing the Champions League," added Bruce.
"They think it's going to clash. Is it going to be a real problem for them? I somehow doubt it."
The replay winners will meet Bruce's former club Sunderland in the quarter-finals.