Messi was among four players in the PSG squad to have tested positive for the coronavirus. Others were left-back Juan Bernat, backup goalie Sergio Rico and 19-year-old midfielder Nathan Bitumazala.
PSG resumed training earlier this week, raising the prospect of further infections in the squad.
In Messi's absence, Kylian Mbappe scored a second-half hat trick to help PSG beat fourth-tier Vannes 4-0 and enter French Cup last 16.
14-time champions PSG are the most successful side in the history of the tournament. They beat Moncao 2-0 in the 2020–21 final.
Last year, Messi won a record-extending seventh Ballon d'Or. He joined PSG from Barcelona on a free transfer last August amid emotional outpouring from the Catalan side. He signed a two-year deal with an option for an extra year.
In 2021, he scored 40 goals for the clubs and the national team, and won the 2021 Copa America -- his first major international title with the Argentina national football team.