The former Mexico international was already left out of Cruz Azul's 1-1 league draw at Club Tijuana on Sunday because of the controversy surrounding the images of the party that went viral on social media.
The Liga MX and Cruz Azul had condemned the veteran defender, who has since apologised.
Dominguez, 35, said in a video statement that "it was a mistake" and accepted the "distress that the images caused to the Mexican society."
Sources have told ESPN that Cruz Azul will not disclose how much the player will be fined for "security reasons."
Dominguez will miss Saturday's home league game against Monterrey and the trip to Necaxa on Jan. 21.