Defensive linchpin Cameron Carter-Vickers has also been named among the substitutes alongside other first team regulars including Liel Abada, Jota, Reo Hatate and Josip Juranovic.
Stephen Welsh has been drafted into the Celtic defence alongside Liam Scales, who takes the place of Greg Taylor at left back, following their recent starts against Raith Rovers in the Scottish Cup.
Nir Bitton captains the side in the absence of McGregor and anchors the midfield while James Forrest returns to the starting line-up.
Giorgos Giakoumakis spearheads the attack after his weekend hat-trick against Dundee with Daizen Maeda set to move onto the left wing.
It is a team selection that suggests Postecoglou may be prioritising Sunday's Scottish Premiership trip to Easter Road to face Hibs as his Celtic side look to maintain their three point advantage in the title race.
Celtic team v Bodo/Glimt: Hart, Ralston, Welsh, Starfelt, Scales, Bitton (c), O'Riley, Rogic, Forrest, Maeda, Giakoumakis. Subs: Bain, Oluwayemi, Jullien, Taylor, Abada, McCarthy, Jota, Carter-Vickers, Hatate, McGregor, Juranovic.