"Lewandowski has a strain in his left hamstring," said Barcelona in a statement, without specifying the length of his expected absence.
Barcelona face Madrid at the Santiago Bernabeu on Thursday in the first leg of the cup tie, already without injured duo Pedri and Ousmane Dembele.
Polish striker Lewandowski, 34, is the team's top scorer with 25 goals across all competitions this season after joining from Bayern Munich last summer.
Spanish news outlet Relevo report Lewandowski is set to miss around two weeks and return before Barcelona face Real Madrid in La Liga on March 19, although other outlets say he may heal quicker.
The second leg of the Copa del Rey clash does not take place until April 5, by when the Catalans expect all their injured players to have recovered.
Barcelona were eliminated from the Europa League by Manchester United last week and suffered a second consecutive defeat on Sunday, against Almeria in La Liga, where it is suspected Lewandowski sustained his hamstring strain.
Xavi Hernandez's side are seven points clear of Real Madrid at the top of the table.
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