The Ivorian made a derogatory remark on his Facebook page about referee Bjorn Kuipers after the Dutchman sent off Zlatan Ibrahimovic in the Champions League game against Chelsea last Wednesday.
Aurier was injured and did not play in the match as PSG drew 2-2 in the last-16 second leg at Stamford Bridge to advance to the quarter-finals on away goals.
"I apologise to Mr Kuipers, his assistants and all the referees for my reaction after the match at Chelsea," Aurier wrote on his Twitter feed on Tuesday.
The disciplinary panel of European football's ruling body UEFA will meet on Thursday to assess the case.
Ibrahimovic is also being investigated by the French League for launching into a foul-mouthed rant after PSG lost 3-2 at Girondins de Bordeaux in Ligue 1 on Sunday.
(Reporting by Julien Pretot, editing by Tony Jimenez)
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