The teenage left-back broke two bones in his left hand when colliding with Carlos Edwards and falling over the advertisement boards at Portman Road during last Saturday's 3-1 defeat to Ipswich.
The injury is not serious but Hancox will play no part against Rovers at St Andrew's.
Wes Thomas also misses out with an ankle injury so boss Lee Clark will add youngsters Akwasi Asante, Koby Arthur and Olly Lee to his squad.
Jonathan Spector, Keith Fahey, Marlon King, David Murphy, Will Packwood and Stephen Carr are long-term absentees.
Club captain Carr on Friday confirmed his retirement from the game.