The L'Equipe newspaper reported that the Argentine superstar would not be able to play or train, and will not be paid while suspended.
Messi will miss the Ligue 1 match against Troyes on May 7 and one against Ajaccio on May 13.
The 35-year-old netted 20 goals and assisted 19 in 37 matches this season.
Messi guided Argentina to the 2022 World Cup title by defeating 2018 champions France 4-2 on penalties in Qatar.
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