An arc extinguishing power device driving apparatus and an arc extinguishing apparatus of the present disclosure belong to the electrical field, and are particularly an arc extinguishing power device driving apparatus applicable to an electronic arc extinguishing apparatus for driving a power device. The power device that needs to be driven is connected in parallel to a mechanical switch that requires arc extinguishing, and includes a first voltage detection switch. An input end of the first voltage detection switch is connected to two ends of the power device. The first voltage detection switch is connected in series in a driving loop of the power device. The first voltage detection switch is turned on when detecting that there is a potential difference between the two ends of the power device. A driving signal is transferred to the power device by using the first voltage detection switch, to drive the power device to be turned on. The first voltage detection switch is a semi-controllable switch, or a fully-controllable switch whose threshold is less than an on-state voltage of the power device. The present disclosure has advantages of no need of a semiconductor device with a high withstand voltage, real-time detection on disconnection of a mechanical switch, and low driving energy consumption.