Messi undertook the trip following PSG's 3-1 home loss to Lorient on Sunday which saw their lead at the top of the table cut to five points.
The 35-year-old went on the trip with his family to fulfill some commercial commitments.
Messi reportedly asked for permission before going on the journey but was refused.
The seven-time Ballon D'or winner will not train with the PSG squad during his period of suspension and will miss upcoming games against Troyes and Ajaccio.
PSG have five games left to play this season but it remains to be seen whether Messi returns to feature in the last three after his suspension.
Messi's contract with PSG expires at the end of the season and has been heavily linked with a return to Barcelona.
The World Cup winner has made 28 appearances in the French top flight this season, scoring 15 goals and providing 15 assists.
