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.
Messi tested positive while on holiday in his hometown of Rosario in Argentina.
“He is constantly in contact with our medical service. When he is negative, he will be able to return to France,” PSG coach Mauricio Pochettino told a press conference.
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 Pochettino said he did not know if he would 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.
Pochettino added: “We have been living with the virus for almost two years, everyone knows what to do in order not to be infected. But we can still catch it, there are things we cannot control.”
Bernat tested positive after reporting for training.
“This is the risk with which we live, on a global scale,” said Pochettino. “In football, contact is inevitable, we share the dressing room.
“The risk of contamination is there, but we take all the necessary measures to try to prevent a player from infecting others.”
The number of Covid cases in France has topped 200,000 a day this week.
PSG also said that Neymar, who suffered an ankle injury in November, is continuing treatment in his native Brazil.
“He is still scheduled to return to training in about three weeks,” the club said.
