Saakashvili denies that the alliance has suspended his country’s membership plans.
Cabinet reshuffle follows summer defeat by Russia over breakaway regions.
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.