It is an object of the invention to provide a magnetic sensor apparatus and a current sensor apparatus each of which incorporates a fluxgate element for reducing an offset voltage and reducing variations in offset voltage. A drive section for exciting a sensor coil (2) includes a self-excited oscillation circuit having a resonant circuit part of which is made up of the sensor coil (2). The self-excited oscillation circuit includes an npn transistor (21) and a pnp transistor (31) that are amplifier elements used for continuing oscillation. The npn transistor (21) operates when an oscillation wave is on the positive side. The pnp transistor (31) operates when an oscillation wave is on the negative side. In the self-excited oscillation circuit, clamping of oscillation waves similarly occurs on both positive and negative sides. Therefore, the oscillation waveform has symmetrical positive and negative portions or has minor asymmetry if any.