The Argentinian forward experienced what Mascherano described as a "minor muscle injury" in his upper right leg during Miami's victory over Necaxa last Saturday.
Although there is no set timeline for Messi's return, Mascherano expressed optimism that the star would be back on the pitch soon.
"Amid the unfortunate news, there is a silver lining," Mascherano told reporters.
"He typically recovers well from injuries and usually does so quickly, so we will see. However, he will definitely not be available for tomorrow. We'll assess how he feels and how he progresses afterward."
Messi, who leads the league with 18 goals in MLS matches this season, guided Miami to the Leagues Cup title in 2023 shortly after joining the Herons.
Inter Miami likely needs a win against Pumas in their final group stage match to qualify for the quarter-finals of the Leagues Cup, which includes teams from both MLS and the Mexican league.
If Miami advances to the knockout rounds, Messi would have two weeks to recuperate before the quarter-finals.
Miami's next MLS game is scheduled for Sunday against Orlando .