We present evidence of a substantial ionospheric response to a strong interplanetary coronal mass ejection (ICME) detected by the Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS) on board the Mars Express (MEX) spacecraft. A powerful ICME impacted the Martian ionosphere beginning on 5 June 2011, peaking on 6 June, and trailing off over about a week. This event caused a strong response in the charged particle detector of the High-Energy Neutron Detector (HEND) on board the Odyssey spacecraft. The ion mass spectrometer of the Analyzer of Space Plasmas and Energetic Atoms instrument on MEX detected an increase in background counts, simultaneous with the increase seen by HEND, due to the flux of solar energetic particles (SEPs) associated with the ICME. Local densities and magnetic field strengths measured by MARSIS and enhancements of 100 eV electrons denote the passing of an intense space weather event. Local density and magnetosheath electron measurements and remote soundings show compression of ionospheric plasma to lower altitudes due to increased solar wind dynamic pressure. MARSIS topside sounding of the ionosphere indicates that it is extended well beyond the terminator, to about 116° solar zenith angle, in a highly disturbed state. This extension may be due to increased ionization due to SEPs and magnetosheath electrons or to plasma transport across the terminator. The surface reflection from both ionospheric sounding and subsurface modes of the MARSIS radar was attenuated, indicating increased electron content in the Mars ionosphere at low altitudes, where the atmosphere is dense.