The tie will take place at Ewood Park on the weekend of January 28th/29th, when Rovers were originally scheduled to face Fulham in the Championship.
Owen Coyle's side booked their place in the draw courtesy of a comfortable 2-1 win away to QPR, whilst Blackpool and Barnsley drew 0-0 in their third round tie at Bloomfield Road.
The game could potentially see a return to Ewood Park for former Rovers manager Gary Bowyer, who took over at Blackpool in the summer and has guided the Seasiders to 11th in League Two, five points off the play-offs.
Rovers faced Barnsley only a fortnight ago, on Boxing Day, when goals from Sam Winnall and Marley Watkins secured a 2-0 victory for Paul Heckingbottom's side, who currently sit eighth in the Championship.
Rovers are unbeaten against both sides in the competition.
Against Barnsley, Rovers have won four and drawn one of the previous five FA Cup encounters, the last one coming during the 2001-02 season when Graeme Souness' side won 3-1 at Ewood Park in a third round replay - Corrado Grabbi, David Dunn (pen) and Nils-Eric Johansson getting the goals - after the game at Oakwell had ended 1-1.
There have been four previous meetings with Blackpool in the competition, with Rovers winning three and drawing one. The most recent meeting was during the famous 1959-60 season when Rovers defeated the Seasiders 3-0 in a replay at Bloomfield Road, en route to reaching the final!
Barnsley and Blackpool will face either other in their third round replay at Oakwell on Tuesday January 17th.
Fourth round draw in full:
Tottenham Hotspur v Wycombe Wanderers
Derby County v Leicester City
Oxford United v Birmingham City or Newcastle United
Sutton United or AFC Wimbledon v Leeds United
Liverpool or Plymouth Argyle v Wolverhampton Wanderers
Norwich City or Southampton v Arsenal
Ipswich Town or Lincoln City v Brighton & Hove Albion
Chelsea v Brentford
Manchester United v Wigan Athletic
Millwall v Watford
Rochdale v Huddersfield Town
Sunderland or Burnley v Bristol City or Fleetwood Town
Rovers v Blackpool or Barnsley
Fulham v Hull City
Middlesbrough v Accrington Stanley
Bolton Wanderers or Crystal Palace v Manchester City