A fuel injector has a valve needle that has a maximum diameter at a flow-off edge, and a valve seat acting together with the valve needle using a sealing seat, the valve seat widening, starting from the sealing seat up to a discharge edge, and the flow-off edge of the valve needle being offset backwards, in relation to the flow direction, with respect to the discharge edge of the valve seat, when the fuel injector is closed. The flow-off edge of the valve needle is offset backwards with respect to the discharge edge of the valve seat in a predetermined range of 2 micrometers to 20 micrometers, in the direction of a longitudinal valve axis.