The 36-year-old was due to captain the county in their final four Division One fixtures, but has been asked to rest a hamstring injury by Cricket Australia.
"We are naturally disappointed that Adam cannot return," said managing director of cricket Angus Fraser.
"He is a fine player and a highly respected member of our squad. His presence will be missed."
Voges has played 18 Tests for Australia and featured in all three games of their recent series defeat by Sri Lanka.
He had made six Championship appearances for Middlesex before that tour, scoring 388 runs.
Championship leaders Middlesex will be without Australia batsman Adam Voges for the remainder of the 2016 season.