The Brazilian playmaker picked up a muscle problem in training that will rule him out of Sunday's game.
Kaka has been heavily criticized by Spanish media for failing to replicate the form that saw him named the 2007 Player of the Year since joining from AC Milan last summer.
But Real manager Manuel Pellegrini, who is also under fire following Real's Champions League elimination at the hands of Olympique Lyon, stood by him.
"He is adapting to a new league and has all my support," the Chilean told a news conference.
"He has provided a good number of goals and assists. He is an example as both a person and a professional, even if we know he can still give more."
The Primera Liga is Real's only chance of silverware this season. They lie on top of the table, ahead of second-placed and arch-rivals Barcelona on goal difference.