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.
Messi said in a broadcast on social media: “Hello. Well, I wanted to make this video after everything that's going on. First of all, I apologise again to my team-mates at the club. I honestly thought that we were going to have the day off after the game as we had done before. I had organised this trip to Saudi Arabia, which I had previously cancelled and I couldn't go. Once again, I apologise for what I did. So here I am, waiting to see what the club wants to do, nothing more. A hug."
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.
