The electron cyclotron drift instability, implicated in electron heating and anomalous transport, is detected in the plasma of a planar magnetron. Electron density fluctuations associated with the mode are identified via an adapted coherent Thomson scattering diagnostic, under direct current and high-power pulsed magnetron operation. Time-resolved analysis of the mode amplitude reveals that the instability, found at MHz frequencies and millimeter scales, also exhibits a kHz-scale modulation consistent with the observation of larger-scale plasma density nonuniformities, such as the rotating spoke. Sharply collimated axial fluctuations observed at the magnetron axis are consistent with the presence of escaping electrons in a region where the magnetic and electric fields are antiparallel. These results distinguish aspects of magnetron physics from other plasma sources of similar geometry, such as the Hall thruster, and broaden the scope of instabilities which may be considered to dictate magnetron plasma features.