The Vanarama National League side earned rich reward for their defeat of Championship Leeds on Sunday when they were handed a visit from Arsene Wenger's side in the draw for the last 16.
National League leaders Lincoln will also face top-flight opposition as they travel to Burnley.
Lincoln have already beaten three league sides in Oldham, Ipswich and Championship leaders Brighton during their cup run.
It is the first time in the history of the competition two non-League sides have reached the last 16.
Sutton's clash will see Arsene Wenger take his men to the 5,000-capacity Gander Green Lane to play on United's 3G pitch.
Elsewhere in the draw, Wolves' reward for knocking out Liverpool on Saturday is a home clash with Premier League leaders Chelsea
Oxford, who also pulled off a giant-killing against Championship high-flyers Newcastle, will travel to Middlesbrough.
Tottenham, after surviving a scare against Wycombe, face an all-London clash at Fulham while holders Manchester United and Manchester City will make the short journeys to Blackburn and Huddersfield respectively.
The final tie of the round will see League One Millwall, conquerors of Watford, host the winners of the replay between Derby and Premier League champions Leicester.
Source : PA