His assistants Jesus Perez and Miguel D’Agostino will take charge of the team for Saturday’s trip to Angers.
Three PSG players had already tested positive for the virus in the last week — Brazilian Rafinha, Germany’s Thilo Kehrer and French youth international Colin Dagba.
Former Tottenham coach Pochettino has overseen three PSG games so far, notably winning the Champions Trophy in Lens on Wednesday thanks to a 2-1 win over bitter rivals Marseille.
Pochettino took over from Thomas Tuchel and signed a contract until June 30, 2022 with an option for an additional year.
Tuchel was sacked on December 24, reportedly for comments viewed as critical of the Qatari owners despite having led the team to a maiden appearance in the Champions League final last season.
Pochettino also played for the Parisians from 2001 to 2003.
France has reeled from more than 2.8 million Covid-19 infections and 69,313 deaths, according to official figures.
From Saturday, a nationwide curfew, starting at 6pm, will be introduced.
Meanwhile, relegation threatened Lorient’s home game against fellow strugglers Dijon was cancelled on Friday after a virus outbreak in the Breton side.
The postponement of Sunday’s game is the first in Ligue 1 since Marseille’s meeting with Nice on November 17 was called off.
“Following advice from the national Covid commission, it was decided to postpone the match due to the absence of more than 10 of 30 Lorient players after positive RT-PCR tests,” the French Football Federation announced.
Under protocols agreed at the beginning of September, matches are postponed if a team does not have 20 players with negative tests available.
Lorient also confirmed their training centre would close for a minimum of 10 days after positive tests from youth players and management.
There are fears the virus may have spread after the Lorient youngsters played a recent friendly against Nantes.
Lorient sit 19th in Ligue 1, are winless in five games, and are two points and one place behind Dijon.
Strasbourg’s match with Saint-Etienne, scheduled for Sunday at the same time as the Lorient v Dijon game, is also under threat of postponement.
Several players and members of the management team at Saint-Etienne have tested positive, said the club.
“The PCR tests carried out Tuesday and Thursday revealed many positive cases for Covid-19 among the players and members of the management of the squad,” said the club in a statement.
Saint-Etienne are currently in 16th place in the table, five points off the drop zone with Strasbourg a place and a point better off.