The seven-time Ballon d'Or winner was one of four PSG players to test positive for the virus ahead of a French Cup match against Vannes.
The Argentinian star has endured a difficult start to life in the French capital since an emotional exit from Barcelona last summer.
Messi has scored only one goal in 11 league appearances for PSG, although he has netted five times in the Champions League.
He will miss Monday's cup tie and will likely also be sidelined for PSG's first Ligue 1 match since the winter break, at Lyon next Sunday.
The other players to test positive were full-back Juan Bernat, back-up goalkeeper Sergio Rico and teenage midfielder Nathan Bitumazala.
"They are currently respecting isolation and are subject to the appropriate health protocols," PSG said.
The number of Covid cases in France has topped 200,000 a day this week.
