The Belgium international will be out of action for several weeks after incurring the injury on Tuesday.
"Courtois will begin his recovery process in the coming days," Real said in a statement.
The 31-year-old was expected to return to Real's squad after spending several months on the sidelines following an ACL tear in his left knee in August.
Courtois made 31 league appearances for Real last season but is yet to play for his club in this campaign.
Real, who are top of the La Liga standings and eight points above rivals Barcelona, host Athletic Bilbao on March 31st.