The governing body stated that Hughes "intimated his decision upon return from holiday and the board respects his decision" ahead of Wednesday's annual general meeting.
Rangers chairman Dave King had already called for Hughes to be suspended by the SFA after a photograph of a 2006 article from The Publican appeared in a newspaper in May.
Hughes, who was then chief executive of the trade magazine's publisher, was credited as writing in a piece on Glasgow pubs: "The next best thing to being at Celtic Park (only the great unwashed venture south to Ibrox) is watching the game, pint of Tennents in hand, with some like-minded souls."
In a statement released by the SFA, Hughes - who joined the organisation in 2015 - said: "It has been an honour and a privilege to bring my professional expertise to the game I love.
"I have been involved in business for 30 years but the commitment of my board colleagues - and indeed everyone involved in Scottish football - to improve the national sport in this country has made it an absolute pleasure.
"I will remain a passionate supporter of the Scottish FA's activities, but it is time to focus on other business interests at home and abroad."
SFA bosses had launched a probe into Hughes's alleged comments when they emerged last month.