An apparatus for igniting a fuel mixture provides an ignition system for generating a high-voltage ignition voltage, a circuit device comprising a circuit for superimposing a high-frequency signal on to the high-voltage ignition voltage, a spark plug in an engine block, and a transmission element having a high-voltage conductor which is guided in an insulation element. The high-voltage conductor is used for transmitting the ignition voltage, onto which the high-frequency signal has been superimposed, to the spark plug. Further provided is an electrically conducting shielding element which surrounds the high-voltage conductor in an electromagnetically shielding manner at least along one portion of the longitudinal axis of the high-voltage conductor. The shielding element is connected in an electrically conducting manner to a ground potential of the circuit device and establishes a connection between the ground potential of the circuit device and a ground electrode of the spark plug.