Footage on social media appeared to show travelling supporters of the Italian side making Nazi salutes and monkey gestures during their Group H opener, which PSG won thanks to a first-half double from Kylian Mbappe.
"In accordance with Article 31(4) of the UEFA Disciplinary Regulations, a UEFA Ethics and Disciplinary Inspector has been appointed to conduct a disciplinary investigation regarding allegations of discriminatory behaviour by Juventus supporters," the body said on Wednesday.
Paris police added that four people had been arrested in connection with the incident.
"Four individuals were identified by video and then arrested last night (Tuesday) by the police for public incitement to racial hatred in a sports venue, on the occasion of the PSG-Juve soccer match," they said in a statement.
The reverse fixture in Turin will be played on November 2nd.