Ben Sulayem has been embroiled in a series of other controversies since he was elected in December 2021.
Robyn did not respond to requests for comment from BBC Sport.
The FIA quoted her in a statement saying: “Performing in the role of CEO at the FIA has been an enormous privilege and I am grateful to have directed a programme of restructuring and reform.
“Now is the time to step away in the knowledge that the organisation is better placed for the challenges which lie ahead.”
The FIA statement said Robyn had “spearheaded a comprehensive overhaul of the federation’s operational structure, playing a pivotal role in modernising the FIA, enhancing governance, and securing sustainable financial stability”.
Robyn, a former car industry executive for Volvo, Nissan and DaimlerChrysler, started work for the FIA in late 2022, and her recruitment was described at the time by Ben Sulayem as “a transformative moment for our federation”.
Ben Sulayem said in a statement about her departure: “Natalie’s appointment was notable as the first CEO in the history of the FIA. She has contributed greatly to a wide-ranging reorganisation of our operational and management structure as well as our financial sustainability.”