The 29-year-old was dismissed in the first half of the 2-2 draw after referee Craig Pawson ruled he had fouled Mame Diouf.
Replays suggested Vardy was knocked off balance by Glen Johnson just before making the tackle on Diouf and the Foxes will make their case to the Football Association
Boss Claudio Ranieri was unhappy with Pawson's first-half performance and confronted the official on the pitch at half-time but is unlikely to face any further punishment
If the Foxes fail in their appeal Vardy will miss Boxing Day's visit of Everton, the home game with West Ham on New Year's Eve and a trip to Middlesbrough on January 2
It was the England striker's second red of the year after he was sent off in last season's 2-2 draw with West Ham in April, with Stoke boss Mark Hughes claiming Vardy was "out of control" when he made the tackle
Leicester manager Ranieri suggested the club would appeal after the game and felt the challenge warranted only a yellow card.
The Foxes face a fine from the FA for having six or more players shown yellow cards in the match at the Britannia Stadium
Robert Huth and Christian Fuchs were booked to collect their fifth cautions of the season and will miss the game against Everton.
Leicester recovered from 2-0 down with 10 men to earn a 2-2 draw after Leonardo Ulloa and Daniel Amartey scored in the final 16 minutes
It was just their second away point of the season with Ranieri's side yet to win on the road in the Premier League and the defending champions 15th in the table.
Source : PA