Large ionospheric variability is found at low to middle latitudes when a quasi‐stationary planetary wave is specified in the winter stratosphere in the National Center for Atmospheric Research thermosphere‐ionosphere‐mesosphere electrodynamics general circulation model for solar minimum conditions. The variability includes change of electric field/ion drift, F2 peak density and height, and the total electron content. The electric field/ion drift change is the largest near dawn in the numerical experiments. Analysis of model results suggests that, although the quasi‐stationary planetary wave does not propagate deep into the ionosphere or to low latitudes due to the presence of critical layers and strong molecular dissipation, the planetary wave and tidal interaction leads to large changes in tides, which can strongly impact the ionosphere at low and middle latitudes through the E region wind dynamo. Large zonal gradients of zonal and meridional winds from the tidal components and the zonal gradient of electric conductivities at dawn can produce large convergence/divergence of Hall and Pedersen currents, which in turn produces a polarization electric field. The ionospheric changes are dependent on both the longitude and local time, and are determined by the amplitudes and phases of the superposing wave components. The model results are consistent with observed ionospheric changes at low and middle latitudes during stratospheric sudden warming events, when quasi‐stationary planetary waves become large.