Hot Jupiters, with atmospheric temperatures T ~ 1000 K, have residual thermal ionization levels sufficient for the interaction of the ions with the planetary magnetic field to result in a sizable magnetic drag on the (neutral) atmospheric winds. We evaluate the magnitude of magnetic drag in a representative three-dimensional atmospheric model of the hot Jupiter HD 209458b and find that it is a plausible mechanism to limit wind speeds in this class of atmospheres. Magnetic drag has a strong geometrical dependence, both meridionally and from the day to the night side (in the upper atmosphere), which could have interesting consequences for the atmospheric flow pattern. By extension, close-in eccentric planets with transiently heated atmospheres will experience time-variable levels of magnetic drag. A robust treatment of magnetic drag in circulation models for hot atmospheres may require iterated solutions to the magnetic induction and Saha equations as the hydrodynamical flow is evolved.