A peripheral pressure sensor for a motor vehicle has a sensor chip and a gasket sealing a sensing unit of the sensor chip from the surroundings, which gasket has a pressure channel through which pressure information is transmitted to the sensing unit of the sensor chip. The peripheral pressure sensor is made by an injection molding method in which an opening in the gasket is placed on the sensing unit of the sensor chip, and subsequently an assembly of the sensor chip and the gasket is surrounded by extrusion coating such that an outer edge opposite the sensing unit and/or an outer opening in the gasket remains at least partially free.