A power unit for a motorcycle includes an internal combustion engine with a transmission having an input shaft and an output shaft. A clutch with a hydraulic cylinder is provided for changing over the connection/disconnection of power transmission between a crankshaft and the input shaft. A cylinder support member, mounted on the engine body, includes a cylindrical case portion where a portion of the hydraulic cylinder is housed. The power unit can be miniaturized by suppressing the projection of the hydraulic cylinder from the engine body in the axial direction. A cover member is mounted on the engine body for covering and surrounding a projecting end portion of an output shaft from an engine body. A cylinder support member is mounted on the engine body such that a portion of a case portion is arranged in an opening portion formed by cutting away a portion of the cover member.