Saakashvili denies that the alliance has suspended his country’s membership plans.
Grigol Vashadze, the culture minister, will become the new foreign minister.
Vashadze will take over from 31-year-old Ekaterine Tkeshelashvili.
Separately, a political source told the Reuters news agency that Irakly Alasania, Georgia’s popular ambassador to the United Nations, had resigned.
Alasania has been touted as a potential challenger to Mikheil Saakashvili, the president.