The defender picked up the problem during Real's 1-1 draw with Real Valladolid on Wednesday and was sent for tests to determine the extent of the problem.
On Friday, the club announced Pepe had suffered a "grade one" injury which could reportedly see him sidelined for up to two weeks, meaning he would face a race against time to be fit for the European final in Lisbon on May 24.
"After receiving imaging tests today, the Real Madrid player Pepe was diagnosed with a grade one injury in the calf muscle of his left leg," the club statement read.
"The player's progress will be monitored."
Real will already be without midfielder Xabi Alonso in the final due to suspension, and not having the Portugal international in defence would be a blow for head coach Carlo Ancelotti.
Pepe has made 48 appearances for Madrid this season in all competitions and could be replaced at the heart of their defence by the fit-again Raphael Varane should he fail to recover in time.
