We report the discovery of a rare close binary system, SMSS J160639.78-100010.7, comprised of a magnetic white dwarf with a field of about 30 MG and a brown dwarf. We measured an orbital period of 92 min which is consistent with the photometric period. Minimum and maximum light occur at the orbital quadratures Phi=0.25 and 0.75, respectively, and cannot be caused by reflection on the brown dwarf, but, instead, by a spot on the synchronously rotating magnetic white dwarf. The brown dwarf does not fill its Roche lobe and the system may be in a low-accretion state or, more likely, in a detached state following episodes of mass transfer. SMSS J160639.78-100010.7 is the nearest known magnetic white dwarf plus brown dwarf system.