Messi sustained the injury during last weekend's Leagues Cup match against Necaxa. There is no timeline for the forward's return.
"No, Leo will not be available tomorrow," Mascherano said Saturday, per ESPN.
"Leo is OK, but obviously it would be crazy to take the risk of taking him to Orlando because of all that is ahead. We are optimistic that he will soon return with us."
Messi, 38, entered this weekend with 18 goals, tied with Sam Surridge of Nashville SC for the lead in the chase for the Golden Boot. The Argentina native also has nine assists in 18 MLS matches (17 starts) this season.
After visiting Orlando City, the Herons will host Los Angeles FC next Saturday before facing Tigres UANL in the Leagues Cup quarterfinals on Aug. 20 in Fort Lauderdale, Fla.