The invention relates to a fuel injector (10) with an injector housing (11) in which an injection member (22) for closing and opening at least one injection opening (16) formed in the injector housing (11) is arranged to be movable in stroke, and with a sensor device (30) for detecting at least the closing time point of the injection member (22), wherein the sensor device (30) has a sensor element (31) designed as a piezo element, which is arranged in a recess (33) of the injector housing (11) in contact with the injector housing (11), and which is designed to detect the closing time point of the injection member (22) on the basis of a structure-borne sound signal. According to the invention, it is provided that the sensor element (31) rests against a contact surface (35) under axial preload.