Kaka, who made his first appearance of the season for the Spanish club in January, had a series of tests which revealed the extent of the knee problem, the team said on their website on Tuesday.
The 28-year-old former AC Milan player will miss Saturday's La Liga match at home to Hercules as well as next week's Champions League last-16 second leg against Olympique Lyon, also at Real's Bernabeu stadium.
Coach Jose Mourinho told a news conference on Saturday it was better for Kaka, who has struggled to regain his best form since his return, to get properly fit before playing again.
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