Vardy is due to miss three games for the struggling Foxes after his red card in a 2-2 draw with Stoke City.
Match referee Craig Pawson infuriated the Leicester players and manager Claudio Ranieri in also booking five players in the final seven minutes of the first half -- Vardy had been dismissed in the 28th minute.
As a result Vardy is due to miss three games for the struggling Foxes whilst key defenders Robert Huth and Christian Fuchs will also be suspended for the next match against Everton after picking up their fifth bookings of the campaign.
"Leicester City have today (Monday) lodged an appeal with the Football Association against the dismissal of Jamie Vardy during Saturday's Premier League fixture at Stoke City," read a statement from the club.
"Jamie was shown a straight red card by referee Craig Pawson in the 28th minute of Saturday's 2-2 draw for a challenge that was deemed to have constituted serious foul play.
"The club has subsequently made its case for an instance of wrongful dismissal and expects to hear the outcome of the appeal in the coming days."
If the appeal fails Vardy will miss next Monday's visit of Everton and then matches with two fellow strugglers, West Ham United on New Year's Eve and a trip to Middlesbrough on January 2.
Ironically Pawson had been criticised for not sending off Manchester United defender Marcos Rojo for a similar two-footed challenge in their Premier League clash with Crystal Palace only a few days prior to the Vardy incident.
Leicester currently sit a lowly 15th in the table, just three points clear of the relegation places.