The draw for the quarter-final was conducted after Wednesday’s matches.
The eight teams left in the FA Cup this season have been drawn against each other.
Manchester United, who came from behind to beat West Ham 3-1, will host Fulham.
Their rivals Manchester City welcome Burnley to the Etihad, while Brighton take on Grimsby.
FA quarter-final draw in full:
Man City vs Burnley
Man Utd vs Fulham
Brighton vs Grimsby
Sheffield Utd vs Blackburn
