Masi assumed the role of race director when predecessor Charlie Whiting died on the eve of the 2019 F1 season
The move comes four months after an FIA inquiry found "human error" was responsible for the incorrect application of the rules in the 2021 title-deciding Abu Dhabi Grand Prix.
Masi has "decided to leave the FIA and relocate to Australia to be closer to his family and take on new challenges".
There was no mention of the Abu Dhabi controversy in the FIA statement.
Masi's failure to follow the sporting regulations during a late safety-car period at Yas Marina resulted in the world championship changing hands.
Mercedes driver Lewis Hamilton was on course to win a record eighth world title, but he was overtaken by Red Bull's Max Verstappen when the race was restarted for one final lap, securing a maiden drivers' crown for the Dutchman.
Masi was removed as race director as part of an FIA restructure in February.
The FIA report listed a number of errors made by the Australian. These included:
The FIA statement said Masi "oversaw a three-year period as FIA Formula 1 race director and safety delegate following the sudden passing of Charlie Whiting in 2019, carrying out the numerous functions he was tasked with in a professional and dedicated manner.
"The FIA thanks him for his commitment and wishes him the best for the future."
FIA president Mohammed Ben Sulayem had previously said he was in talks with Masi with the aim of finding him another role within the organisation.
However, Masi declined to continue with the FIA and insiders have told BBC Sport he felt he had lacked support from the organisation in the wake of the events in Abu Dhabi.
A number of changes have been put in place following the Abu Dhabi race to try to ensure similar mistakes are not made again.
These include splitting the role of race director between two people; an extended team in race control; the establishment of a virtual race control to support the one at the track, and preventing teams directly communicating with the race director.
It was found in the report that interventions from Mercedes and Red Bull - including from team principals Toto Wolff and Christian Horner - "had a negative impact on the smooth running of the final laps because they were distracting when the race director needed to focus on making difficult and time-pressured decisions".
-- Courtesy of BBC Sport