Premier League champions Leicester City will travel to Derby County in an East Midlands derby, while Chelsea meet Brentford in a west London derby.
League One Millwall's reward for beating Bournemouth is to host another Premier League side, Watford.
The winners of the replay between Liverpool and League Two Plymouth will be at home to Wolverhampton Wanderers of the Championship.
Sutton United, the lowest-ranked side left in the competition, will face Leeds United - if they win their replay against AFC Wimbledon.
The fourth round represents the last-32 stage of the competition, and all ties are scheduled to be played from 27-30 January.
Draw in full:
Tottenham Hotspur v Wycombe Wanderers
Derby County v Leicester City
Oxford United v Newcastle United or Birmingham City
AFC Wimbledon or Sutton United v Leeds United
Plymouth Argyle or Liverpool v Wolverhampton Wanderers
Southampton or Norwich City v Arsenal
Lincoln or Ipswich v Brighton
Chelsea v Brentford
Manchester United v Wigan Athletic
Millwall v Watford
Rochdale v Huddersfield Town
Burnley or Sunderland v Fleetwood Town or Bristol City
Blackburn Rovers v Barnsley or Blackpool
Fulham v Hull City
Middlesbrough v Accrington Stanley
Crystal Palace or Bolton v Manchester City
Holders Manchester United will host 2013 winners Wigan Athletic in the fourth round of the FA Cup.