The suspension starts immediately and means he will miss this month's CONCACAF Gold Cup being held in the United States.
The disciplinary committee of soccer's world governing body found Osorio guilty of "using insulting words towards the match officials while displaying an aggressive attitude towards them" in the match, which Mexico lost 2-1 on July 2.
Osorio was angered after match officials decided not to refer an apparent push on Mexico's Hector Moreno for an assessment by the Video Assistant Referee (VAR). He led the protests and was sent to the stands.
The 56-year-old was found to have breached Article 49.1 a) of the FIFA Disciplinary Code, warned about his behaviour and fined 5,000 Swiss francs ($5,183.50) on top of the ban.
Osorio begins his suspension with the CONCACAF Gold Cup Group C game against El Salvador on July 10. If Mexico reach the final Osorio will have served the ban at the tournament.
If they do not get that far the remaining matches of the ban will be served in Mexico's subsequent official internationals.
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 Russia.
The Gold Cup, played once every two years, showcases the 12 teams that qualified through regional tournaments in the North American, Central American and Caribbean regions.
Mexico are also due to play Jamaica and Curacao in the group stage. The top two teams from each of the three sections plus the two best third-placed teams qualify for the quarter-finals.
($1 = 0.9646 Swiss francs)
(Reporting by John Revill; additional reporting by Neil Robinson; Editing by Brenna Hughes Neghaiwi and Ken Ferris)
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