Preliminary estimates show that consumer prices passed the 5% mark for the first time since June 1992, when a post-reunification economic boom drove inflation up 5.8%.
Inflation was at 4.5% year-on-year in October.
The energy crunch was the most significant factor behind the rise in the cost of living in Germany. Destatis estimated that energy prices were up more than 22% in November, compared to the same month last year.