The Brazilian was substituted after 34 minutes during PSG's 3-2 victory over Marseille in Ligue 1 on Sunday, and now faces around a month out of action.
Coach Laurent Blanc said on Tuesday: "David Luiz will be sidelined for four weeks and Thiago Motta for 10 days following their injuries against Marseille.
"It will take us time to deal with the injuries we have. Nevertheless, we will play to win all our matches."
Blanc also has concerns over Serge Aurier, Edinson Cavani, Lucas and Zlatan Ibrahimovic ahead of a busy month for PSG.
The French champions play Saint-Etienne in the Coupe de France semi-final on Wednesday, before then taking on Bastia in the Coupe de la Ligue final on Saturday.
The home leg of their last eight clash with Barca comes on April 15, before the return game against Lionel Messi and co six days later.
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