A bumper crossmember for a motor vehicle having a crossmember extending transversely to the longitudinal axis of the vehicle and two crashboxes connected thereto. Each crashbox is connected with its end facing away from the vehicle to the crossmember in a respective end section thereof, and with its end facing the vehicle is connectable to a structural component of the vehicle, e.g., a longitudinal member. The crossmember has a corrugated structure in the area where a crashbox is connected. A tow sleeve is integrated into the bumper crossmember in the connection area of the crashbox. The tow sleeve is held in a vertex structure of the corrugated structure in a form-fitting manner in the z and y directions, the vertex area of this vertex structure facing away from the crashbox, with the lateral surface of the tow sleeve on the flanks facing one another and forming the vertex structure.