A fuel injector includes a solenoid coil, which cooperates with an armature acted upon by a restoring spring, the armature forming an axially displaceable valve part together with a valve needle. A valve-closure member, which forms a sealing seat together with a valve-seat body, is provided on the valve needle. Furthermore, a reliable sealing of a thin-walled valve sleeve or of the magnetic coil exists that is made of a sealing body that is secured beneath the magnetic coil. The sealing body is tetragonal in cross-section, in particular, it has a trapezoid-like shape, and is put in between the magnetic coil and a valve housing. In its installed state, the sealing body is clamped and compressed. In its compressed state, the sealing body assumes an elliptical or egg-shaped cross-section.