Fellow non-League side Lincoln City also drew top-flight opposition in Burnley, who they will face at Turf Moor.
The FA Cup has never had two teams from outside the Football League in its fifth round until this season, with Lincoln seeing off Championship title contenders Brighton & Hove Albion before Sutton stunned Leeds United - similarly perched in the second tier - at Gander Green Lane.
#EmiratesFACup - initial reaction from Chairman along the lines "we would take a replay"— Sutton United FC (@suttonunited) January 30, 2017
Whether 12-time winners Arsenal will rock up at the 5,000 capacity ground - plastic pitch and all - remains to be seen, but the fixture will be Sutton's most prestigious ever regardless of venue.
And Paul Doswell's men have history on their side, with Sutton's win over Coventry City in 1989 representing the last time a non-league team beat top-flight opposition on home turf in the FA Cup.
Lincoln eliminated Ipswich Town as well as Brighton en route to the fifth round, but their visit to Burnley is a daunting challenge - only Chelsea, Tottenham and Arsenal have picked up more home Premier League points than the Clarets this season.
Each of the eight Premier League sides remaining in a competition of shocks have been kept apart, with Wolves hoping to add Antonio Conte's Chelsea to the list of Premier League clubs they have knocked out after beating Stoke City and Liverpool.
FA Cup fifth round draw in full:
Burnley v Lincoln City
Fulham v Tottenham
Blackburn Rovers v Manchester United
Sutton United v Arsenal
Middlesbrough v Oxford United
Wolves v Chelsea
Huddersfield v Manchester City
Millwall v Derby County or Leicester City
Ties are due to be played between Friday, February 17 and Monday, February 20.