United's path would have been clearer had they not surrendered a two-goal lead to the holders in Sunday's quarter-final but Sir Alex Ferguson's side must now travel to Stamford Bridge for another try.
Championship pair Millwall and Blackburn must also go again after their goalless draw, with the winner of Wednesday's decider at Ewood Park to take on Wigan Athletic.
The relegation-threatened Latics reached the last four of the competition for the first time with a 3-0 win at Everton on Saturday, while Manchester City booked a second appearance in three seasons thanks to a 5-0 thumping of Barnsley.
Wigan chairman Dave Whelan described a potential Wembley date with Blackburn - the team he turned out for in the 1960 final only to break his leg in the first half - as a "dream".
"All Blackburn have got to do now is get through the replay and my dream is on," Whelan told Sky Sports News. "I feel I've got unfinished business at Wembley.
"Roberto (Martinez) has asked me to lead them out at Wembley and if we get Blackburn, I may just say yes."
United and City met in the FA Cup semi-final in 2011, while City and Chelsea have not faced off in the competition since 1971, when the north-west side won 3-0 in London.
"We have to think about the first game and, afterwards, think about City," Chelsea boss Rafa Benitez said after Sunday's 2-2 draw. "It will be tough, will be difficult, United are a great side."
FA Cup semi-final draw:
Millwall or Blackburn Rovers v Wigan Athletic
Manchester United or Chelsea v Manchester City
Ties to be played at Wembley on the weekend of 13/14 April.