Corrosion is normally an undesirable phenomenon in engineering applications. In the field of biomedical applications, however, implants that 'biocorrode' are of considerable interest. Deploying them not only abrogates the need for implant-removal surgery, but also circumvents the long-term negative effects of permanent implants. In this context magnesium is an attractive biodegradable material, but its corrosion is accompanied by hydrogen evolution, which is problematic in many biomedical applications. Whereas the degradation and thus the hydrogen evolution of crystalline Mg alloys can be altered only within a very limited range, Mg-based glasses offer extended solubility for alloying elements plus a homogeneous single-phase structure, both of which may alter corrosion behaviour significantly. Here we report on a distinct reduction in hydrogen evolution in Zn-rich MgZnCa glasses. Above a particular Zn-alloying threshold ( 28 at.%), a Zn- and oxygen-rich passivating layer forms on the alloy surface, which we explain by a model based on the calculated Pourbaix diagram of Zn in simulated body fluid. We document animal studies that confirm the great reduction in hydrogen evolution and reveal the same good tissue compatibility as seen for crystalline Mg implants. Thus, the glassy Mg60+xZn35−xCa5 (0≤x≤7) alloys show great potential for deployment in a new generation of biodegradable implants.