A cover for a spare wheel arranged externally at the rear of a motor vehicle has a clamping strap which covers the entire tread of the tire. In its lateral edge regions, the clamping strap is drawn in towards the center of the wheel. A round plate covers the free side of the wheel. Over the peripheral edge region of the plate, the drawn-in edge region of the clamping strap engages. In order to make such a cover easy to mount for a single person and to permit it to be used simultaneously for different tire widths, there is provided an outer, annular region of the plate bent to extend towards the spare wheel. A support body can be inserted into a vehicle-side receptacle as far as a stop. The support body is attached to the center of the rear of the plate. The length of the support body is dimensioned such that, when tightening the clamping strap, the plate, acting so to speak as a disc spring, presses the support body against its stop.