The 38-year-old was one of the main antagonists as the two sets of players confronted each other following Inter Miami’s 3-0 Leagues Cup defeat to Seattle Sounders.
Suarez has since been handed a six-game suspension after spitting at a Sounders staff member.
Teammate Sergio Busquets got two games due to violent conduct and young Inter Miami defender Tomas Aviles got three, also for violent conduct.
Seattle assistant coach Steven Lenhart received a five-game ban for violent conduct.
Suarez and Busquets are both out of contract at the end of the year, with serious doubts about whether they will renew their deals.
