League leaders Leicester have also accepted the charge of failing to control their players after both they and Vardy had until 6pm on Thursday to respond.
Vardy is already banned for Sunday's match at home to Swansea City and is now in line to receive a longer ban, meaning he is almost certain to be kept out of the match at Manchester United on May 1.
The exact punishments handed out to Leicester and the 29-year-old will now be determined by a three-man independent commission.
The club's statement read: "Leicester City Football Club has accepted a Football Association charge of failing to control its players during the Barclays Premier League fixture against West Ham United on 17 April.
"Furthermore, Jamie Vardy has accepted a charge of improper conduct arising from the same fixture. Jamie has, however, requested a personal hearing.
"We await the outcome of the FA's disciplinary process."
The England international was given a second yellow card for simulation having gone to ground in the penalty area following a tangle of legs with Angelo Ogbonna in last Sunday's match.
Vardy was incensed with referee Jon Moss and angrily shouted at the official before leaving the pitch.
Prior to his guilty plea, Vardy had seen Roy Hodgson leap to his defence, the England manager saying he did not feel the striker had dived and said the reaction of the Foxes star to the decision of Moss was "only human".
If Leicester had opted to challenge the charges, they could have received heavier punishments if their appeals proved to be unsuccessful.