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.
Both club and player have until 6 p.m. on Thursday to respond to the charges, the FA said.
(Reporting by Simon Jennings in Bengaluru; Editing by Ken Ferris)
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