Barcola was substituted in the 59th minute by Desire Doue in PSG's 3-0 hammering of Chelsea for an 8-2 aggregate win in their last-16 tie, having scored the second goal of the night.
PSG will play either Liverpool or Galatasaray in the quarter-finals with the first leg being played on April 7 or 8.
The injury is likely to also rule the 23-year-old Barcola out of France's friendly games against Brazil and Colombia next week.