Bezhuashvili, will not be in the new Cabinet due to be formed following the January 5 snap presidential polls, a foreign ministry spokeswoman said on Thursday.
"After talks with the president [Saakashvili], Bezhuashvili decided not to take up a place in the new Georgian administration," she said, without giving further details.
Georgian President Mikheil Saakashvili was forced to step down in late November and call early elections after riot police in the capital, Tbilisi, had clamped down on opposition protesters demanding his resignation over corruption allegations.
At the subsequent January 5 elections Saakashvili received 53.47% of the vote and was inaugurated on January 20.
Georgian media said David Bakradze, Georgia's acting state minister for conflict settlement and head of the election headquarters of Mikheil Saakashvili's second election campaign, was now the leading candidate for the post of foreign minster.
Georgian acting prime minister, Lado Gurgenidze, is expected to present a list of candidates for ministerial posts to the president on Thursday evening.
