The Owls will visit Queens Park Rangers in the next stage of the competition.
The two sides have already met this season with Mark Warburton’s side winning 2-1 at Hillsborough.
Their has been only one previous FA Cup meeting between the two sides with Wednesday winning 3-0 at home in the third round in January 1967.
Wednesday earned their place in the fourth round with a 1-0 win at Premier League side Brighton and Hove Albion on Saturday.
Fourth round ties will be played on the weekend of January 24 with scheduled dates to be confirmed later this week.
Fourth round draw in full:
Watford or Tranmere v Wolves or Manchester United
Hull v Chelsea
Southampton v Middlesbrough or Tottenham
QPR v Sheffield Wednesday
Bournemouth v Arsenal or Leeds
Northampton v Derby
Brentford v Leicester
Millwall v Sheffield United
Reading or Blackpool v Cardiff or Carlisle
West Ham v West Brom
Burnley v Norwich
Bristol Rovers or Coventry v Birmingham
Manchester City v Fulham
Rochdale or Newcastle v Oxford
Portsmouth v Barnsley
Bristol City or Shrewsbury v Liverpool