Manchester United's reward for beating holders Chelsea in Monday's final fifth-round tie is a FA Cup quarter-final tie at Wolves.
Premier League champions Manchester City are at Championship side Swansea City, with another second-tier side Millwall at home to Brighton.
Watford host Crystal Palace in the other last-eight tie.
DRAW RESULTS:
Swansea vs Man City
Watford vs Crystal Palace
Wolves vs Man Utd
Millwall vs Brighton
The quarter final ties will take place between Friday 15 March and Monday 18 March with winning clubs receiving £720,000 in prize money.