A magnetic field sensor includes: a circuit board having a first surface, a second surface opposite to the first surface, and a recess extending from the first surface to the second surface; a Hall sensor component having a Hall sensor situated in a housing, the Hall sensor component having an active sensor area situated parallel to the first surface and in the area of the recess on the side of the second surface on the circuit board; and a first magnetic flux concentrator made of a magnetically permeable material and situated on the side of the first surface opposite to the Hall sensor component, the magnetic flux concentrator having a lateral surface which faces away from the circuit board and includes a first surface area and a lateral surface which faces toward the circuit board and includes a second surface area which is smaller than the first surface area.