The invention relates to a device for cleaning teeth of a human or animal user with a mouthpiece to be placed in the user's mouth, having a support with cleaning elements arranged thereon, which cleaning elements are arranged on the support for simultaneous engagement with substantially all of the teeth of an upper jaw and/or a lower jaw of the user, and with an electric drive unit fastened detachably to the mouthpiece with at least one vibration element to execute a vibrating motion, wherein the cleaning elements are arranged on the support for simultaneous engagement with substantially all of the teeth of the upper jaw and the lower jaw of the user, and that a detachable magnetic connection is provided for the detachable fastening of the drive unit to the mouthpiece.