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Uruguay failed to escape Group H despite the 2-0 win over Ghana, as Korea Republicx advanced at its expense after its comeback victory over Portugal.
Diego Alonso's team was eliminated on the basis of goals scored, and reacted angrily when Cavani was denied a late penalty after going down in the Ghana 18-yard box.
Social media footage showed the former Manchester United striker pushing the VAR monitor over after the final whistle, while several other Uruguay players surrounded referee Daniel Siebert.
FIFA detailed the charges, alleging misconduct of Uruguayan players and officials, offensive behaviour and discrimination, in a statement.
The statement also said Uruguay quartet Cavani, Godin, Jose Gimenez and Fernando Muslera were being investigated separately for alleged offences relating to offensive behaviour, violations of the principles of fair play and misconduct.
Speaking after the game, which almost certainly marked the end of his World Cup career, striker Luis Suarez declared: "FIFA is always against Uruguay".
In a separate statement, FIFA revealed Serbia would also face charges of misconduct, discrimination and failure to preserve order and security after its fractious 3-2 defeat to Switzerland on the same day.
Serbia's loss ensured it finished bottom of Group G, while Switzerland advanced to the last 16 by joining pre-tournament favourite Brazil on six points.