The Portuguese centre-back has travelled to his homeland for treatment but is expected to return for the reigning Spanish champions when they take on the Red Devils
The 29-year-old felt discomfort in his right ankle and travelled to Porto for a consultation on Wednesday morning which ended in doctors deciding on medical intervention.
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The first leg of Real's last-16 tie will take place at the Santiago Bernabeu, with the return leg scheduled for March 5 at Old Trafford.
Pepe has played a crucial role for Los Blancos so far this term, making 16 league appearances for Jose Mourinho's side.