However QPR are currently fifth in the Championship, 17 places and 22 points ahead of Posh. They beat League One promotion contenders Rotherham United on penalties in yesterday’s third round while Posh were edging past League Two strugglers Bristol Rovers 2-1.
The tie will take place between February 4-7.
Posh have only been drawn against QPR once in the FA Cup. Posh won a second round replay 2-1 in the 1964-65 season thanks to two goals from Peter Deakin, the second in extra time. The teams had drawn 3-3 at Loftus Road with the Posh goals coming from Deakin, Ron Barnes and Peter McNamee.
Posh went on to beat Division One giants Arsenal in the fourth round on the way to a club record sixth round (quarter-final) appearance. Posh lost that tie 5-1 at Chelsea.
Posh progress in the FA Cup means the Championship fixture against Luton Town scheduled for Saturday, February 5 will be postponed.
Full fourth round draw: Crystal Palace v Hartlepool, Bournemouth v Boreham Wood, Huddersfield v Barnsley, Peterborough v QPR, Cambridge v Luton, Southampton v Coventry, Chelsea v Plymouth, Everton v Brentford,
Kidderminster v West Ham, Man Utd or Villa v Middlesbrough, Spurs v Brighton, Liverpool v Cardiff, Stoke v Wigan, Nottingham Forest or Arsenal v Leicester, Man City v Fulham, Wolves v Norwich.