A sensor for measuring a flow speed of a fluid medium includes a housing with a carrier membrane disposed in the housing and being essentially in a form of a vane having a circumference and at least one edge region. Holding elements are arranged over a portion of the circumference connecting the vane to the housing so that only the at least one edge region of the carrier membrane is subjected to mechanical stress caused by the housing. An electrically conductive track with feed lines is installed on the carrier membrane in a region of a neutral fiber for the carrier membrane which does not experience a mechanical strain when the carrier membrane is bent. The electrically conductive track is adapted for being heated relative to the environment by an electrical current flowing through the electrically conductive track.