Known sensor supports have a recess in which a sensor element is glued by means of an adhesive. The device according to the invention has a plate-shaped sensor element that is accommodated in a recess of a sensor support. A sensor region (3) has at least one measurement resistor, which region is exposed to the flowing medium wherein a gap remains between the sensor element and the recess. To protect an evaluation circuit connected to the sensor element against moisture, the provision is made, according to the invention, that at least partial regions of the evaluation circuit and partial regions of the sensor element are covered by a protective coating, wherein the gap has at least one enlargement by means of which the flow of the protective coating can be influenced. The device according to the invention is used for measuring the mass of a flowing medium in the intake air mass of internal combustion engines.