United remain in the competition after Sunday's dramatic penalty shootout win against Arsenal.
The victory sees United now host Leicester City after the Fourth Round draw was made on Sunday evening.
Aston Villa will face Tottenham, while giantkillers Plymouth will host Liverpool after dumping out Brentford.
FA Cup Fourth Round Draw:
Manchester United v Leicester City
Leeds United v Millwall or Dagenham and Redbridge
Brighton & Hove Albion v Chelsea
Preston North End or Charlton Athletic v Wycombe Wanderers
Exeter City v Nottingham Forest
Blackburn Rovers v Wolverhampton Wanderers
Mansfield Town or Wigan Athletic v Fulham
Birmingham City v Newcastle United
Plymouth Argyle v Liverpool
Aston Villa v Tottenham Hotspur
Leyton Orient or Derby County v Manchester City