The magnetic field in the anode plasma of a magnetically insulated ion-beam diode has been measured as a function of time by the observation of Zeeman splitting of line emission. With use of this technique, the plasma was found to be penetrated by the magnetic field applied in the diode early in the pulse. The diamagnetic effect of the electron flow in the diode acceleration gap was found to be much larger than that calculated from one-dimensional solutions for the magnetically insulated gap. However, it agrees with the measured ion current density and the observed electric field distributions across the diode gap that showed significant electron flow beyond the calculated electron-sheath region. The penetration of the diamagnetic signal into the plasma indicates an anomalous plasma conductivity that is at least ten times lower than the classical conductivity.