United, who comfortably beat Arsenal 2-0 at Old Trafford on Saturday evening, were drawn against the winners of the sixth-round tie between City and Reading.
City eventually triumphed 1-0 over the Royals on Sunday afternoon thanks to Micah Richards' second-half header, securing the Manchester derby date at Wembley.
Roo beauty: United booked their place in the last four with a 2-0 win over Arsenal on Saturday evening
Stoke sealed their first FA Cup semi-final in 39 years after they edged past West Ham 2-1 at the Britannia Stadium.
The Potters will play Bolton who beat Carling Cup holders Birmingham in a thrilling encounter at St Andrews on Saturday.
FA CUP SEMI-FINAL DRAW Manchester City v Manchester United
Bolton Wanderers v Stoke City
The ties will be played on the weekend of 16 and 17 April at Wembley Stadium.
Stoke 2 West Ham 1: Danny Higginbotham calls time on Hammers FA Cup dreamBirmingham 2 Bolton 3: Davies keeps alive the spirit of legend LofthouseManchester United 2 Arsenal 0: Rooney snuffs out Wenger's Wembley bid
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