The Skrill Premier side held League One outfit Peterborough to a 0-0 draw on Saturday and will make the trip to Wearside later in the month if they can win the replay after Gus Poyet's side beat Carlisle 3-1.
Rochdale's reward for knocking Leeds out of the competition is a home draw with either Kidderminster's fellow non-league side Macclesfield or Sheffield Wednesday.
League One strugglers Stevenage have landed a plum tie with Everton, while Sheffield United, who pulled off one of the shocks of round three by beating Aston Villa 2-1 away from home, will entertain the winners of the replay between Norwich and Fulham at Bramall Lane.
Southend will host Steve Bruce's Hull after defeating Millwall 4-1 on Saturday, while holders Wigan will take on Crystal Palace at the DW Stadium, providing they can first see off MK Dons.
Elsewhere, Coventry will get the chance to try and upset Arsenal at the Emirates and Bolton play Cardiff at the Reebok Stadium and Brendan Rodgers will take his Liverpool side to either Bournemouth or Burton.
Last year's beaten finalists Manchester City will host either Bristol City or Watford if they win their replay against Blackburn.
Swansea must wait to find out their opponents after their dramatic victory over Manchester United at Old Trafford.
Bristol Rovers' second-round replay with Crawley on Saturday had to be abandoned due to a waterlogged pitch, further delaying their third-round clash with Birmingham, the winners of which will face Swansea.
In the only all-Premier League tie, Chelsea will entertain Stoke after Jose Mourinho's side defeated Derby 2-0 at Pride Park.
FA CUP FOURTH-ROUND DRAW:
Sunderland v Kidderminster
Bolton v Cardiff
Southampton v Yeovil
Huddersfield v Charlton/Oxford
Port Vale/Plymouth v Brighton
Nottingham Forest v Preston
Southend v Hull
Rochdale v Sheffield Wednesday
Arsenal v Coventry
Stevenage v Everton
Wigan v Crystal Palace
Chelsea v Stoke
Man City v Watford
Bournemouth/Burton v Liverpool
Birmingham/Bristol Rovers/Crawley v Swansea
Sheff Utd v Norwich/Fulham
Ties to be played the weekend of 25 and 26 January