Using Mars Global Surveyor magnetometer/electron reflectometer measurements, we report initial observations of low-frequency magnetic fluctuations in the Martian ionosphere. We find that the waves have dominant frequencies between 0.01 and 1 Hz and are observed both close to and far from crustal magnetic fields. These waves are possibly related to magnetosonic perturbations produced at higher altitudes in the Mars--solar wind interaction. These fluctuations have implications for understanding the physics of the ionosphere and potentially could also help characterize electromagnetically active atmospheric phenomena such as dust devils and dust storms. The presence of such fluctuations in the Martian ionosphere is also an indication of the plausibility of using low-frequency electromagnetic methods, such as the magnetotelluric technique, to probe the deep subsurface. One potential result of such an investigation would be the identification of any subsurface liquid water that might be present within the first several hundred meters to the first few kilometers of the subsurface.