The former AEK Athens keeper was badly at fault for the Midtjylland equaliser last week and followed that up with another unconvincing display against West Ham on Saturday.
Postecoglou had spoke warmly about Barkas during the pre-season but facing a crunch match in Denmark he has turned to Bain in a bid to keep Celtic on course for the group stage of the Champions League.
Apart from Bain it is the same side that faced Midtjylland last week with Dane Murray replacing the suspended Nir Bitton.
Celtic are a man short on the substitute bench with Leo Hjelde failing to be listed leaving Osaze Urhoghide as the only central defensive option.
CELTIC: Bain, Ralston, Welsh, Murray, Taylor; Soro, McGregor; Abada, Turnbull, Christie; Edouard
SUBS: Barkas, Doohan, Ajeti, Rogic, Bolingoli, Urhoghide, Shaw, Robertson, Forrest, Montgomery