Brighton booked their place in the final four of the competition with a 5-0 thrashing of League Two side Grimsby Town.
Meanwhile, City face Championship club Sheffield United, who beat Blackburn Rovers on Sunday. Pep Guardiola's side face second-tier opposition for the second time in a row, after knocking out former club captain Vincent Kompany's Burnley with a 6-0 win on Saturday.
United boss Erik ten Hag is looking to add to the Carabao Cup trophy he has already won in his debut season at Old Trafford. The Dutchman has the chance to win three pieces of silverware this campaign with the club also still in the Europa League.
Guardiola's side can also win three trophies this season. City face Bayern Munich in the Champions League quarterfinals but are eight points behind Arsenal in the Premier League title race.
The semifinals will be played at Wembley Stadium on April 22-23 with the final to be played on June 3.
FA Cup semifinal draw:
Brighton & Hove Albion vs. Manchester United
Manchester City vs. Sheffield United