Hull, who are bidding for a hat-trick of Wembley triumphs, will be away to the Championship club on the weekend of May 11-13.
It will be the first Challenge Cup meeting between the two clubs since 1983, when the West Yorkshire side pulled off a shock 14-12 win at Wembley.
Rovers, who are second in the Championship after winning nine of their opening 11 matches, will be hoping to repeat their heroics of 2012 when they knocked Castleford out of the cup.
Warrington, Cup winners three times in four years from 2009-12, were drawn away to Canadian outfit Toronto Wolfpack but because of the logistics will have home advantage, much to the delight of Wolves fan Chris Evans, who made the draw on his BBC Radio 2 Breakfast Show.
The tie will mean a reunion for Fiji international Ashton Sims, who made the move from Warrington to Toronto at the end of last season.
Super League bottom club Catalans Dragons, who were pushed all the way by York in the fifth round, landed a home tie against another League 1 club, Whitehaven, the lowest-ranked team left in the last 16.
Leigh, the other surviving Championship club, have a tasty home tie against Salford while 19-times winners Wigan will start out against Hull KR at Craven Park.
Two of the ties will be broadcast by the BBC, with two more shown by Sky, and one of the televised games is sure to be Castleford’s encounter with Super League leaders St Helens.
Saints will have the chance to avenge a humiliating 53-10 hammering by the Tigers in the corresponding stage of the 2017 competition.
The draw also produces a Yorkshire derby as Huddersfield Giants host Wakefield Trinity, while Leeds go to Widnes, aiming to avenge a recent league defeat.
The draw for the sixth round of the Ladbrokes Challenge Cup is (matches to be played May 12-13):
Hull KR v Wigan Warriors
Castleford Tigers v St Helens
Toronto Wolfpack v Warrington Wolves (to be played at Warrington)
Leigh Centurions v Salford Red Devils
Featherstone Rovers v Hull FC
Catalans Dragons v Whitehaven
Widnes Vikings v Leeds Rhinos
Huddersfield Giants v Wakefield Trinity