Ousmane Dembele's double and Fabian Ruiz's strike earned PSG a comeback win on Saturday. Brest had taken the lead just before the half-hour mark after a foul by Mendes on Ludovic Ajorque resulted in a penalty which was converted by Romain del Castillo.
Portuguese left-back Mendes posted a screenshot of a racist message sent to him on social media and the club said they are working with authorities to hold those responsible accountable.
"Paris St-Germain doesn't tolerate racism, anti-Semitism or any other form of discrimination," the club said in a statement late on Sunday. "The racial insults directed at Nuno Mendes are totally unacceptable.
"We stand firmly by Nuno and all those affected and we are working with the relevant authorities and associations to ensure those responsible are held accountable for their actions."
PSG face Girona in the Champions League on Wednesday and travel to Stade de Reims on Saturday in the French League.
