The Uruguayan football federation has also been fined 50,000 Swiss francs (£43,814) and handed a partial stadium closure for their next home match over the "discriminatory behaviour of its supporters" and the "misconduct" of the players.
Uruguay were incensed by refereeing decisions during their 2-0 win over Ghana in their final group game in Qatar last December.
A three-goal win would have seen them qualify for the last 16 but they were knocked out in dramatic fashion.
Referee Daniel Siebert was hounded by players after the match, while Cavani punched the pitchside VAR monitor.
Defender Jose Maria Gimenez and goalkeeper Fernando Muslera have both been banned for four matches, fined 20,000 Swiss francs (£17,524) and given "community football service".
Veterans Cavani and Godin were given one-match bans each, will have to perform community service and were fined 15,000 Swiss francs (£13,144).
