Argentina international Messi joined PSG from boyhood club Barcelona in August and the 34-year-old has scored six goals in 16 games in all competitions for the Parisian side.
Defender Juan Bernat, back-up goalkeeper Sergio Rico and midfielder Nathan Bitumazala were the other players who returned positive tests.
Mauricio Pochettino's team are top of the Ligue 1 standings on 46 points after 19 matches, 13 points above second-placed Nice. They are due to travel to third-tier club Vannes tomorrow for a French Cup round-of-32 match.
