Chelsea boss Mourinho claimed the Gunners have been given an easier ride with the Premiership fixture list and insinuated that the presence of Dein on the FA's board had implications for the Blues.
The FA branded Mourinho's comments "unnecessary, unhelpful, bad for the image of the game and inaccurate".
In May, Mourinho was fined £200,000 by the Premier League over the Ashley Cole tapping-up saga Chelsea were also fined £300,000 after a complaint by Arsenal but he insists his club get a raw deal.
However, the FA statement goes on to point out that Dein has no influence on the FA's disciplinary bodies.
It said: "The Arsenal vice-chairman David Dein is one of four members of the FA board representing the FA Premier League. The four Premier League representatives are elected by the 20 member Premier League clubs (including Chelsea) to represent their views within the FA.
"We would like to state categorically that Mr Dein does not have any involvement within the FA's disciplinary or compliance functions. It should also be made clear that he is not a member of the FA's disciplinary committee.
"Therefore, Mr Dein does not have any input into any decisions to charge individuals or clubs with breaches of FA rules, nor in any judgement or punishment administered by a disciplinary commission."
Mourinho could yet find himself in disciplinary trouble again before a ball has even been kicked in the new season as the FA are scrutinising the remarks to see whether they warrant any action.
Meanwhile, Chelsea's determination to sign Michael Essien is being severely tested by Lyon but the Premiership champions remain confident they will recruit the Ghanaian international.
Essien was yesterday named in Lyon's squad for the Peace Cup, staged in South Korea from July 15-24, as the French club strengthened their resolve to secure the highest possible price for the coveted 22-year-old.
An initial £15.8million bid for Essien was turned down and Chelsea have increased their offer to £16million as Jose Mourinho attempts to land a player who has also attracted interest from Manchester United.