Messi will not train or play with the first team and will not be paid during his suspension.
First reported by French newspaper L'Equipe, PSG manager Christophe Galtier told his players that they would have two days off, Monday and Tuesday, if they beat Lorient on Sunday, but a defeat would result in the players being called in for training on Monday.
Messi, 35, asked if he would be allowed to travel to the Arab gulf to honour his sponsorship deal as a Saudi ambassador, and Galtier and sporting director Luis Campos gave him the green light to go in the result of a win or draw, but not a defeat.
However, following PSG's humbling 3-1 defeat to Lorient -- their third loss in their past four league games -- Messi flew to Saudi Arabia without asking again for permission, sources told ESPN, meaning he could not attend training on Monday.
Sources told ESPN the situation created tensions within the dressing room, with some players unhappy with the incident.
The situation surrounding the World Cup winner is further complicated by his ongoing negotiations over a contract extension.
Messi's deal at the Parc des Princes is due to expire at the end of the season.
Barcelona are looking into the possibility of re-signing Messi, although LaLiga president Javier Tebas warned that the league won't change its financial fair play rules to allow him to return. He is also subject to interest from Saudi Arabian club Al Hilal and Major League Soccer side Inter Miami.