The fuel injection system has one high-pressure fuel pump and one fuel injection valve for one cylinder of the engine. The fuel pump has a work chamber, and the injection valve has a valve member, and which is movable in an opening direction, counter to the force of a closing spring, by the pressure in a pressure chamber communicating with the pump work chamber; the closing spring is braced between the injection valve member and a displaceable deflection piston which, defines a prechamber that communicates with the pump work chamber. The deflection piston is movable into a storage chamber counter to the force of the closing spring. The prechamber communicates with the pump work chamber via a first throttle restriction, and the pressure chamber of the fuel injection valve communicates with the pump work chamber via a second throttle restriction, circumventing the prechamber.