The Scot was a prominent member of FIA president Mohammed Ben Sulayem's team, with the Emirati expected to seek re-election in December.
The resignation, after Reid and Motorsport UK head David Richards opposed the governing body's recent statute changes, will be a talking point ahead of the weekend's Bahrain Formula 1 Grand Prix.
"When I took on this role, it was to serve the FIA’s members, not to serve power," Reid, the 2001 world rally champion co-driver, said in a statement.
"Over time, I have witnessed a steady erosion of the principles we promised to uphold. Decisions are being made behind closed doors, bypassing the very structures and people the FIA exists to represent.
"My resignation is not about personalities; it is about principles. Motorsport deserves leadership that is accountable, transparent, and member-driven. I can no longer, in good faith, remain part of a system that does not reflect those values."
There was no immediate reaction from Ben Sulayem, who is due to attend F1 meetings and the Grand Prix at Sakhir, but an FIA spokesman said a statement was being prepared.
Reid also called on the FIA's member clubs and stakeholders to demand greater accountability from the federation’s leadership.
Richards, currently in the Middle East, wrote an open letter to Motorsport UK members on Wednesday referring to "a shift of the moral compass" at the FIA leadership and said he hoped to discuss matters with Ben Sulayem.