The Scottish champions visited the Allianz Arena on the back of victory away to Anderlecht but were completely overwhelmed by their rejuvenated hosts.
In contrast to their last European outing - a 3-0 dismantling by Paris Saint-Germain - Bayern looked full of confidence from the kickoff after making a winning start to Jupp Heynckes' fourth reign as manager by thrashing Freiburg 5-0 at the weekend.
They thought that they were ahead after just six minutes when Thiago Alcantara finished emphatically from 12 yards out, but Robert Lewandowski was dubiously adjudged to have run the ball out of play before crossing for the Spaniard.
Lewandowski should have had a penalty two minutes later when his shirt was pulled by Mikael Lustig as Celtic resorted to desperate measures to weather the early Bayern storm.
However, the visitors could only survive until the 17th minute when Muller knocked home the rebound after Craig Gordon had saved from Lewandowski's free header.
Kimmich rewarded Bayern's total domination with a second goal before the half-hour mark, planting a pinpoint header across Gordon from Kingsley Coman's cross.
Celtic got through the remainder of the first half unscathed, but were put to bed six minutes after the interval as an unchallenged Hummels met Arjen Robben's corner to guide a header inside the side-netting.
Munich threatened to run riot as Cristian Gamboa, who endured a torrid evening marking Coman on the Celtic right, cleared off the line from Robben's header. Bayern then had a second goal disallowed as the offside flag ruled out Lewandowski's cushioned finish from David Alaba's cross.
As the match went on Celtic came just as close to adding to the scores, as Bayern goalkeeper Sven Ulreich tipped Kieran Tierney's 30-yard shot onto the post, and then saved from Scott Sinclair and substitute James Forrest.
Sinclair did bend a shot beyond Ulreich on 88 minutes, only for Celtic to be denied a consolation by the offside flag.
The only positive for Celtic is that they did not surrender to an even heavier defeat, which was in part down to Gordon who made a great double stop from Robben and Lewandowski, and saved his best for stoppage time when he blocked Arturo Vidal's header from point-blank range.
The result sees Bayern move clear of Celtic in second, three points behind Group B leaders PSG, who put four past Anderlecht tonight. Celtic will be left to fight the Belgians for third place, and the Europa League.