The Gunners are rewarded for beating Tottenham with another home game, while Stevenage will aim to claim a famous scalp against Everton.
The Gunners will host the League One outfit after beating north London rivals Tottenham 2-0 in the third round on Saturday.
Elsewhere, Chelsea takes on Stoke City at Stamford Bridge if it gets past Derby County on Sunday and Everton travels to League One Stevenage, while Southampton hosts Championship side Yeovil.
Manchester City will host Watford or Bristol City if it is able to overcome Blackburn Rovers in a third round replay, while Manchester United or Swansea will travel to Brimingham City, Bristol Rovers or Crawley.
Should it overcome Oldham, Liverpool will face an away match against Bournemouth or Burton Albion.
FA Cup fourth round draw in full:
Sunderland or Carlisle vs. Kiddermister or Peterborough
Bolton vs. Cardiff City
Southampton vs. Yeovil Town
Huddersfield Town vs. Charlton or Oxford United
Port Vale or Plymouth vs. Brighton
Nottingham Forest vs. Ipswich or Preston
Southend vs. Hull City
Rochdale vs. Macclesfield or Sheff Weds
Arsenal vs. Coventry City
Stevenage Borough vs. Everton
Wigan or MK Dons vs. Crystal Palace
Derby or Chelsea vs. Stoke City
Blackburn or Man City vs. Bristol City or Watford
Bournemouth or Burton Albion vs. Liverpool or Oldham
Birmingham or Bristol Rovers or Crawley vs. Manchester United or Swansea
Sheffield Utd vs. Norwich or Fulham