The defeat is the first of Froch's 27-fight professional career and he will now need to beat Germany's Arthur Abraham in his next fight to secure a place in the semi-finals of the Super Six super-middleweight tournament.
That fight was expected to take place in August, but the savage nature of his bout with Kessler might mean it is put back until later in the year.
As for Kessler, who lost to Wales' Joe Calzaghe in 2007, the victory probably saved his career following his emphatic defeat at the hands of American Andre Ward last December.
Froch needed to assert himself from the opening bell to quieten a fiercely partisan crowd at the 10,000 capacity Messecenter, but it was Kessler who spent the first few rounds coming forward, even if he was not landing with much.
The first third of the fight was tight, with the 31-year-old Kessler stalking the champion and fighting behind his stiff left jab and Froch looking a little ragged on the back foot.
Trainer Robert McCracken implored Froch to up his work-rate at the end of the fourth and he looked to have Kessler down in the fifth, but referee Michael Griffin ruled it a slip.
It was over the next four rounds that Froch let the fight get away from him, with Kessler coming forward in straight lines and planting jabs and hurtful rights to the body and Froch unable to nullify him.
Froch's low-slung jab was a limp imitation of the challenger's and in the eighth the champion was stiffened by a huge overhand right from Kessler, although Froch recovered his composure well.
Kessler landed with a sweet uppercut in the ninth and looked to nick that round, although Froch managed to open up a deep cut over Kessler's left eye and the Dane, looking a little flustered, proceeded to lose the following round.
With Froch's corner sensing their man might be in need of a knockout, the 11th unravelled into a wild affair, with Kessler exploding a huge right hand on Froch's neck and Froch surging back before the bell.
Both men looked set to drop in the final round, with Kessler landing with a big left and Froch retaliating with a massive right that had Kessler tottering backwards with 30 seconds to go.
But the immensely game Kessler stayed on his feet and while a couple of the judges' scorecards looked far too lop-sided, Froch could have few arguments with the outcome.
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