The charge arose following his behaviour during the match, in Moscow, on July 2, and a statement from Federation Internationale de Football Association reads: "Mr Osorio used insulting words towards the match officials while displaying an aggressive attitude towards them". He led the protests and was sent to the stands.
If Mexico is eliminated before the Gold Cup final, Osorio would serve his suspension in Mexico's September World Cup qualifiers against Panama and Costa Rica.
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Should Mexico play fewer than six games at the Gold Cup, Osario's suspension will carry over into their next global matches.
In addition to the ban, which is effective immediately, Osorio was warned about his conduct and fined 5,000 Swiss francs ($5,183.50), Federation Internationale de Football Association said.
Last month, Osorio apologised for another outburst, this time directed at the opposing bench during Mexico's 2-1 group victory over New Zealand at the Confederations Cup in Russian Federation.
The biennial tournament kicks off this weekend in the United States and features North America, Central America and Caribbean nations.