A pressure sensor comprising: a solid metal sensor body, having a front region and a base adjoining thereto, which has an outer edge, which can be clamped by means of a fastening device; a recess, which is provided in the front region and is open towards a front side of the front region that faces away from the base; a metal measuring diaphragm, to which a pressure is applied from outside during measurement operation and which can be deformed elastically depending upon the pressure, is arranged on the front side of the sensor body, closes off the recess from the outside, and is spaced apart from the outer edge of the front region; and an electromechanical transducer for detection, by means of measuring the pressure-dependent deformation of the measuring diaphragm, having at least one measuring element, which is electrically insulated from the measuring diaphragm and the sensor body by means of an insulating element.