City's 3-0 victory over a youthful Arsenal side at Eastlands on Wednesday night saw them join their local rivals in the hat for the draw.
- Manchester City 3-0 Arsenal
- Wednesday night results
Holders United were 2-0 winners over Tottenham Hotspur 24 hours earlier and the two north-west heavyweights were pitted against one another in a mouth-watering draw.
The two-legged semi-final will begin at the City of Manchester Stadium on January 5 or 6 with the second leg at Old Trafford two weeks later.
"They are going to be two fantastic games and the whole of Manchester will be tuning in and looking forward to some fantastic games," said City boss Mark Hughes, whose side were beaten 4-3 by United in a thrilling Premier League game back in September.
"Over two games we'd fancy our chances against anyone left in the draw, so bring them on."
Meanwhile, the other semi-final sees Blackburn Rovers take on Aston Villa.
Rovers overcame Chelsea on penalties following a six-goal thriller at Ewood Park on Wednesday night.
Benni McCarthy's extra-time penalty was equalised by Paulo Ferreira with virtually the last kick of the match to take the quarter-final tie to spot-kicks.
But Chelsea's luck ran out there as Gael Kakuta - the French youngster whose controversial move to Stamford Bridge led to a two-year transfer ban - drilled his penalty straight at Paul Robinson to hand Blackburn a 4-1 spot-kick success.
Villa had swept Premier League strugglers Portsmouth aside 4-2 on Tuesday night to book their own place in the last four.