The experienced Toulon back suffered a broken ankle in Australia's 42-8 thrashing by world champions New Zealand in the opening game of the Rugby Championship on Saturday.
Boudjellal confirmed that Giteau was to return to France ahead of surgery on Monday.
Giteau, who has won 103 caps for the Wallabies, had already been ruled out of the rest of the Rugby Championship, with doubts now surrounding his international future.
The 33-year-old was one of three Australia backs to depart the action through injury in the first half on a terrible day for coach Michael Cheika.
Giteau has been with French Top 14 club Toulon for five years, winning three European titles.