The Portugal international limped out of Saturday's 5-0 victory over Almeria holding his left leg, and underwent hospital scans on Monday to determine the extent of the injury.
A statement from the Liga side read: "Following imaging tests to our player Cristiano Ronaldo ... at the hospital Sanitas La Moral, a lesion in the posterior part of the left thigh was detected."
It is unclear how long the 28-year-old will on the sidelines but it looks likely he will not be involved for the visit of the Turkish champions on Wednesday.
The loss of Ronaldo, who has scored 25 goals in 18 Real games this season, represents a major blow for Real, but coach Carlo Ancelotti has an array of stars ready to take his place
Youngsters Jese Rodriguez, Alvaro Morata and Casemiro have all made appearances in recent weeks, with Angel di Maria and Isco also options for the Italian.
Madrid only need a point from the game to ensure their progression to the knockout stages of the competition.
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