The complete elastic tensor of Fe0.94O (wüstite) has been determined to 10 GPa using acoustic interferometry at GHz frequencies inside a diamond-anvil cell. The soft mode (C44) elastic constant of FeO is reduced by 20% over the experimental pressure range. An unusual discontinuity in the pressure derivatives of C11 and C12 at 4.7+/-0.2 GPa corresponds to the pressure at which the onset of a magnetic ordering transition is observed by high-pressure Mössbauer spectroscopy and neutron powder diffraction. Our new results combined with literature structural high P-T data suggest that there is a magnetic, although still cubic, phase of FeO between approximately 5 and approximately 17 GPa.