Leicester have also been charged with failing to control their players after West Ham were awarded a penalty in the 83rd minute at the King Power Stadium on Sunday, the FA added in a statement.
Vardy was shown a second yellow card early in the second half for simulation and appeared to confront referee Jon Moss before leaving the field.
Leicester title challenge dented by West Ham after Vardy sees red
Both club and player have until 6 pm on Thursday to respond to the charges, the FA said.
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