Mechanical spectroscopy is employed, in correlation with differential scanning calorimetry and hydrogen sorption analysis, to investigate the hydrogen desorption reaction in nanostructured magnesium hydride prepared by ball milling. The hydrogen desorption process is marked by a dramatic drop of the specimen's resonance frequency and by an internal friction peak that occurs – under high vacuum – at about 580 K. After full hydrogen desorption, a broad anelastic relaxation peak similar to commercial Mg is observed at 470 K, with activation energy close to the one for self-diffusion in Mg.