The invention is directed to an apparatus for detecting a rotation of a rotational member. A core is disposed opposite to the rotational member. A coil of wire is disposed around the core. A permanent magnet, which is formed in a shaft of a symmetrically cut out cross section, is connected to the core. A bobbin is provided with a first cylindrical portion for receiving therein the core and winding the wire of the coil around the first cylindrical portion, and a second cylindrical portion integrally connected to the first cylindrical portion in co-axial relationship therewith. The second cylindrical portion is formed with cutout portions to provide a periphery corresponding to a periphery of the permanent magnet, and arranged to receive therein at least a part of the permanent magnet in co-axial relationship with the core. A case, which is formed in a cylindrical body for receiving therein the bobbin assembled with the core, permanent magnet and coil, defines a certain space between an outer surface of the second cylindrical portion at the cutout portions thereof and an inner surface of the case. A terminal electrically connected to the coil, is disposed in the space and fixed to the second cylindrical portion.