Planetary magnetosheaths are characterized by high plasma wave and turbulence activity. The Martian magnetosheath is no exception; both upstream and locally generated plasma waves have been observed in the region between its bow shock and magnetic boundary layer, its induced magnetosphere. This statistical study of wave activity in the Martian magnetosheath is based on 12 years (2005–2016) of observations made during Mars Express (MEX) crossings of the planet’s magnetosheath — in particular, data on electron density and temperature data collected by the electron spectrometer (ELS) of the plasma analyzer (ASPERA-3) experiment on board the MEX spacecraft. A kurtosis parameter has been calculated for these plasma parameters. This value indicates intermittent behavior in the data when it is higher than 3 (the value for a normal or Gaussian distribution). The variation of wave activity occurrence has been analyzed in relation to solar cycle, Martian orbit, and distance to the bow shock. Non-Gaussian properties are observed in the magnetosheath of Mars on all analyzed scales, especially in those near the proton gyrofrequency in the upstream region of the Martian magnetosphere. We also report that non-Gaussian behavior is most prominent at the smaller scales (higher frequencies). A significant influence of the solar cycle was also observed; the kurtosis parameter is higher during declining and solar maximum phases, when the presence of disturbed solar wind conditions, caused by large scale solar wind structures, increases. The kurtosis decreases with increasing distance from the bow shock, which indicates that the intermittence level is higher near the bow shock. In the electron temperature data the kurtosis is higher near the perihelion due to the higher incidence of EUV when the planet is closer to the Sun, which causes a more extended exosphere, and consequently increases the wave activity in the magnetosheath and its upstream region. The extended exosphere seems to play a lower effect in the electron density data.