The court ordered Motorola to pay a yet-to-be-specified fine and pull the infringing devices, which run on Google's Android operating system, from the market.
The patent involves a feature known as "overscroll bounce" or "rubber-banding" that pulls a written text or image back to the centre of the screen to signify to the user that the end of a list or menu has been completed.
Motorola, which had won a similar patent case in western Germany last July, has one month to appeal the decision.
The case is just one of many patent battles that technology companies have waged worldwide, but especially in Germany where patent protection laws are particularly strict.
In August, a California court decided in favour of Apple in a patent case against Samsung, awarding the iPhone maker about one billion dollars (euros) in damages.