Following narrow defeats to Ukrainian side Sevastopol and Romanian outfit Cluj, Neil Lennon's team were dismantled by the German outfit and were lucky not to suffer a heavier defeat ahead of the second-qualifying first leg at the Northern Irish champions next week.
In an open first half, Nikola Djurdjic grabbed a double for the home side, one with a contentious penalty, and Kevin Kraus scored another with Georgios Samaras and Mikael Lustig notching replies for the Parkhead men.
Numerous substitutions were made by both sides in the second half but it was Celtic who struggled to cope.
Dominick Drexler added a fourth after the break as the Champions League group hopefuls went to pieces with Baye Djiby Fall netting a fifth from the spot and a sixth near the end with a free header.
Celtic play Union Berlin on Friday in the final fixture of their German tour and Lennon will hope for better before travelling to Belfast.