Cup holders City, who won 2-1 against United in the English Premier League earlier this month, will play an away game against United in the last week of October after their 2-1 win at Swansea here on Wednesday.
Mourinho's United defeated Northampton Town 3-1 also on Wednesday.
The Manchester Derby was not the only heavyweight tie, with Liverpool and Tottenham Hotspur also set to do battle for a place in the quarter-finals.
Meanwhile, there will be a London derby between West Ham United and Chelsea, who won a dramatic third-round tie 4-2 against Leicester in extra time on Tuesday.
Norwich beat Everton and will face Leeds while Preston, who defeated Bournemouth, will play against Newcastle.
Arsenal host Reading while Hull face Bristol City. Southampton face off against Sunderland.
Here is the full draw of the fourth round
West Ham United v Chelsea
Manchester United v Manchester City
Arsenal v Reading
Liverpool v Tottenham
Bristol City v Hull
Leeds United v Norwich City
Newcastle United v Preston NE
Southampton v Sunderland