McKennie and Montes are suspended for four matches by the governing body for football in North America, Central America and the Caribbean, while Dest and Arteaga are banned for three - including an automatic one-match ban.
Montes was sent off before the United States were reduced to 10 men when midfielder McKennie was red-carded following a melee.
The game then spun out of control, with Dest and Arteaga being sent off and the match being paused due to homophobic chants in the crowd. The United States emerged victorious thanks to a Christian Pulisic double that helped secure a 3-0 win over Mexico.
McKennie and Dest are not part of the United States squad for the forthcoming Gold Cup, while Montes and Arteaga are included in Mexico's roster.
It was not immediately clear if McKennie and Dest missing the games will count toward their suspension. Reuters has contacted US Soccer for a comment.
CONCACAF also sanctioned the football federations of the two countries.
"The Committee has imposed an undisclosed fine on both Federations and warned them that more severe sanctions could be taken should incidents occur during their upcoming matches in CONCACAF national team competitions," CONCACAF said in a statement on Friday.
The United States beat Canada 2-0 over the weekend in Las Vegas to win their second successive Nations League title.
