Queensland coach Ewen McKenzie must now choose between utility back Ben Lucas and goalkicking inside centre Mike Harris to start at five-eighth against the Sharks.
Lucas started at No.10 in the last match the Reds played without Cooper, a rousing 42-27 win over the Chiefs, who finished as New Zealand conference winners.
Cooper's loss follows similar bad news for the Sharks who were forced to leave rising Springboks star Patrick Lambie at home in Durban due to an ankle injury.
The Sharks had also hoped to include powerful inside centre Frans Steyn, a late-season recruit, but their appeal to have him eligible was rejected under SANZAR guidelines.
The qualifying final winners at Suncorp Stadium will meet the Chiefs in next week's semi-final in Hamilton.
South African referee Jonathan Kaplan has been appointed to control the Reds-Sharks play-off while compatriot Jaco Peyper will officiate in the Crusaders-Bulls qualifying final in Christchurch.
- AAP