When subjected to cyclic loading, bulk metallic glasses tend to exhibit fatigue-induced damage. Although fatigue is a key limitation of metallic glasses, its atomic origin remains elusive. Here, based on molecular dynamics simulations, we investigate the response of metallic glasses prepared with varying cooling rates to oscillatory stress. We find that fatigue manifests itself as an accumulation of residual strain, which results from some nonaffine displacement of the atoms. Such local reorganizations are promoted under a high cooling rate. Importantly, we demonstrate that the fatigue-induced dynamics of the atoms is encoded in the topography of the static energy landscape, i.e., before any load is applied.