Thin ribbons of the metallic glass Mg65Cu25Y10, obtained by spinning, were saturated with atomic hydrogen from electrochemical decomposition of water. The maximum amount of absorbed hydrogen was 4 mass %. The hydrogen content was determined by hot extraction. We studied the microstructure of samples with different hydrogen contents by x-ray phase analysis (from the change in the diffuse maximum), atomic force microscopy, scanning electron microscopy, and transmission electron microscopy. When the hydrogen content increases up to 3.6 mass %, the amorphous structure of the Mg65Cu25Y10 alloy is converted to a nanocrystalline structure, with formation of magnesium and yttrium hydrides at room temperature.