Manchester United's reward for beating holders Chelsea in Monday's FA Cup fifth-round tie is a quarter-final trip to Wolves.
Premier League champions Manchester City are at Championship side Swansea City, with Millwall - another second-tier side - at home to Brighton.
Watford host Crystal Palace in the other last-eight tie.
The quarter-final games will be played from 15-18 March, with winning clubs receiving £720,000 in prize money.
United saw off Chelsea with a 2-0 victory at Stamford Bridge.
FA Cup quarter-final draw in full
Swansea City v Manchester City
Watford v Crystal Palace
Wolves v Manchester United
Millwall v Brighton