Larry Turner resigned as a councillor in the Kangaroo Island Council on Wednesday morning.
Mr Turner said he was resigning for family reasons and that he may elaborate further on his reasons later.
He was voted back into the council with 148 first-preference votes at the last election in November 2018.
"I do not regret standing, nor do I regret my decision," he said.
Mayor Michael Pengilly said his advice was that one resignation did not require a by-election to fill the position.
However, if there were more than one resignation, then a by-election would be required.
The cost of a by-election to fill two vacancies could be $20,000, he said.
"Council resources are scarce, so any avoidance of a by-election can't be exaggerated."