Injector for injecting fluid

An injector (1) for injecting fluid with a valve comprising a valve body (5) and a valve needle (9) and with a damping element (19) is specified. The damping element (19) is arranged within a cavity (7) of the valve body (5). It comprises a hydraulic chamber (7c), a piston (23) being arranged axially movable relative to the valve body (5) such that it is operable to modify a fluid volume of the hydraulic chamber (7c) and being coupled with the valve needle (9) such that the piston reduces the fluid volume of the hydraulic chamber (7c) when the valve needle (9) moves away from a closing position for unsealing the valve, and a flow restricting orifice (29a) hydraulically connecting the hydraulic chamber (7c) to the cavity (7).