Whiteley picked up the injury in the 42-25 quarter-final victory over the Crusaders last weekend and his loss is a blow for coach Johann Ackermann both in terms of his work with the ball and his leadership qualities.
The captain's armband moves to flank Jaco Kriel with the coach's son, Ruan Ackermann, taking over at the back of the scrum.
That is the only change to the starting line-up announced on Thursday from the side that thumped the Crusaders, though loose-forward Steph de Witt and scrumhalf Dillon Smit come onto the bench.