The game, at LD Nutrition Stadium, is one of four games that will be shown live.
Championship club Featherstone are flying high in the second tier and it is the first time the clubs have met in the Challenge Cup since Rovers’ famous shock 1983 Wembley win over the Black and Whites.
BBC Sport will broadcast two games over the weekend starting with Castleford Tigers v St Helens on Saturday May 12 (2.30pm) followed by Warrington Wolves against Toronto Wolfpack on Sunday May 13 (3.30pm).
Leigh Centurions v Salford Red Devils will also be shown on Sky Sports on Friday May 11 (7.35pm).
In 2015, the Championship side defeated the Red Devils 22-18 at Leigh Sports Village in the fifth round of the competition.
The Ladbrokes Challenge Cup quarter-final draw will be conducted live on BBC Sport at the Halliwell Jones Stadium following the completion of the Warrington Wolves v Toronto Wolfpack fixture.
Confirmed Ladbrokes Challenge Cup sixth round TV schedule:
Thursday, May 10 – Featherstone Rovers v Hull FC (7.35pm, Sky Sports)
Friday, May 11 – Leigh Centurions v Salford Red Devils (7.35pm, Sky Sports)
Saturday, May 12 – Castleford Tigers v St Helens (2.30, BBC One)
Sunday, May 13 – Toronto Wolfpack v Warrington Wolves (3.30pm, BBC Two)*