The other three players are Juan Bernat, Sergio Rico and Nathan Bitumazala.
All players are “in isolation and are subject to the appropriate health protocol,” the team said.
PSG is scheduled to face Vannes in the French Cup’s round of 32 on Monday.
France registered 232,200 new cases of Covid-19 on Friday, the highest daily number registered across Europe since the beginning of the pandemic, according to data from the country’s Health Ministry.
Although comparatively it might be considered a relatively down year at club level for Messi, the 34-year-old Argentine played a vital role in helping Argentina win the Copa América title earlier this year.
He also finished as the Spanish league’s top scorer and scored two goals as Barca won the Copa del Rey.
Neymar injury update
Neymar suffered ligament damage after spraining his ankle during a 3-1 league win over St Etienne in November.
The Brazil international’s return to training is expected to be in about three weeks, said PSG.
Mia Alberti contributed to this report.