The Brazil centre-back was forced off just 13 minutes into the Acqua Lete Cup friendly clash at Stadio San Paolo and limped to the dressing room with heavy strapping on his right leg.
Silva's injury is a blow to coach Laurent Blanc, who handed a debut to big-money signing David Luiz on Ezequiel Lavezzi and Edinson Cavani's respective returns to Naples.
Cavani, whose future with the French champions has been the subject of much speculation, was ineffective before being replaced by Zlatan Ibrahimovic at half-time and Lavezzi was given a great reception by the Napoli fans when he was replaced just after the hour-mark.
Gonzalo Higuain put the Serie A club in front just six minutes after being introduced as a half-time substitute, but Sweden captain Ibrahimovic levelled soon after having also scored twice in PSG's 2-2 draw at Reims in their Ligue 1 opener on Friday.
Javier Pastore then won it with a fine individual goal 13 minutes from time, but Silva's injury overshadowed the victory.
PSG were caught napping 11 minutes before the break when Duvan Zapata's header was cleared off the line, then captain Marek Hamsík's vicious volley was well saved by Salvatore Sirigu.
Michu had another fine volley palmed away by Sirigu early in the second half, but fellow substitute Higuain was on hand to put Rafael Benitez's side in front 51 minutes in after the Italy goalkeeper had kept out Lorenzo Insigne's left-footed strike.
Ibrahimovic then made his mark three minutes later, as he poked the ball home in typically clinical fashion after Rafael could only get his fingertips to a cross from the left.
Lavezzi was given a rapturous reception when he was brought off after 62 minutes and Insigne almost put Napoli back in front but was denied by a fine fingertip save.
David Luiz then had a downward header saved as PSG went in search of a winner, which duly arrived when Pastore picked the ball up and drove into the penalty area before finding the back of the net with a fine finish.
PSG will go in search of their first Ligue 1 win of the season against Bastia on Saturday, while Napoli face a UEFA Champions League play-off first leg clash with Athletic Bilbao next Tuesday.
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