The World Endurance Championship website said the injury happened in a game a week ago, before two Formula E rounds in Berlin last weekend.
It said he would be replaced by Italian Michele Rugolo.
A regular contender for the overall Le Mans LMP1 title in past years with Audi, finishing on the podium three times, Di Grassi had been due to race a Ferrari GT car this year.
The next Formula E race is in New York on July 15. Di Grassi is second in the electric series with 125 points, behind Switzerland's Sebastien Buemi on 157.
The Brazilian twice finished on the podium in Berlin and started one race from pole.
(Reporting by Alan Baldwin in London, editing by Neville Dalton)
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