The club are without overseas star Jake Lehmann for the match at Lord’s, starting on Tuesday, after he was recalled by South Australia to prepare for their domestic season.
But their request for Bairstow to be made available ahead of the forthcoming Bangladesh tour has been rejected by England director of cricket Andrew Strauss and coach Trevor Bayliss - despite the player insisting that he wants to play and is feeling refreshed.
Yorkshire have been dealt a further blow after Adil Rashid requested to be rested from the Middlesex match ahead of the winter tours - even though England have given him permission to play.
In a statement on the Bairstow decision, the club said: “The Yorkshire County Cricket Club would like to express its disappointment after the ECB refused the Club’s request for Jonny Bairstow to participate in the final Specsavers County Championship fixture of the season.
“Yorkshire members, supporters and other stakeholders in the game will wonder why this permission has been refused.
“Having been rested for 16 days since he last played for England, Bairstow said he felt refreshed and wanted to play for Yorkshire against Middlesex at Lord’s, where the club has the opportunity of winning three successive County Championships, a feat last achieved almost 50 years ago.
“Although not a centrally contracted player for the last 12 months, Yorkshire required clearance from the ECB to play Bairstow.
“The club’s director of cricket Martyn Moxon contacted the England hierarchy, but has been refused permission to play Bairstow by director of England Cricket Andrew Strauss and England coach Trevor Bayliss.
“Moxon works closely with England due to the fact that six players from Yorkshire have represented their country regularly over the last 12 months.
“Bayliss’s approach has been to see how the player feels, and this was respected when Bairstow said that he needed a rest after the Royal London One-Day Series.
“To put matters into context, other centrally contracted players who are soon to tour Bangladesh and India with England, have been allowed to represent their county in critical matches.
“Bairstow has played five days of cricket in five weeks since the Kia Oval Test match, which finished on Sunday August 14.”
Yorkshire squad to face Middlesex (starting on Tuesday): Gary Ballance, Tim Bresnan, Jack Brooks, Andrew Gale (captain), Andrew Hodd, Alex Lees, Adam Lyth, Steven Patterson, Liam Plunkett, Azeem Rafiq, Ryan Sidebottom, Jack Leaning, David Willey.