In beating Championship strugglers Charlton Athletic 2-0 on Sunday, United became the first third-tier team to reach the semi-finals since Wycombe Wanderers in 2001.
And Nigel Clough's side have avoided the two biggest clubs left in the competition, Premier League title contenders Arsenal and Manchester City.
Arsenal and City will go head-to-head if the latter see off holders Wigan Athletic in their quarter-final tie, a rematch of last year's final.
United face Hull, who defeated Sunderland 3-0 to reach the last four and are the only team remaining in the competition not to have won the FA Cup previously.
The semi-final ties will take place at Wembley on April 12 and 13.
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