We use seismic data recorded by the NASA InSight mission to constrain the radial seismic attenuation structure of the Martian mantle. Several of the recorded signals cover 3 octaves, between 0.125 and 2~Hz, allowing us to directly measure the spectral decay of seismic energy. Inversion of differential body wave travel times and measured body wave spectra for seismic wave speeds and quality factors QS and QP, respectively, shows that most body waves (P, PP, S, SS) propagate through the upper mantle (100–500 km depth), whereas constraints below 500 km depth stem from by S waves that are reflected at the bottom of the solid mantle. Within the uncertainties of the data, our results indicate little variation in attenuation with depth with mantle QP and QS values in excess of 2000 and 7000, respectively. Above 80~km depth, the observation of very high-frequency seismic energy from impacts requires QS ~ 10000.