The Celeste failed to make it out of Group H in Qatar despite winning its last game 2-0 against Ghana, with Korea Republic advancing at its expense having scored more goals.
Uruguay was fuming when Cavani was denied a late penalty after going down in the Ghana area and the Valencia striker pushed the vidao assistant referee (VAR) monitor over after the final whistle, while several of his team-mates surrounded referee Daniel Siebert.
FIFA on Saturday (AEDT) revealed Cavani and captain Godin have been hit with a one-match suspension, while they must also participate in community football service and pay a fine of $23,000.
Atletico Madrid defender Jose Gimenez and Galatasaray goalkeeper Fernando Muslera have been banned for four games by the world governing body, while they have been hit in the pocket to the tune of CHF $30,532 and also ordered to do community football service work.
The FIFA disciplinary committee also found the Uruguayan FA was responsible for the discriminatory behaviour of its supporters at the 3 December (AEDT) game, as well as for the misconduct, offensive behaviour and violation of the principles of fair play shown by players.
That will result in Uruguay playing its next game with a partial stadium closure, with no fans allowed behind the goals at each end, a FIFA statement read.
The Uruguayan FA has also been fined $76,330.