Understanding the cavity formation and cavity growth mechanisms in solids has fundamental and applied importance for the correct determination of their exploitation capabilities and mechanical characteristics. In this work, we present the molecular dynamics simulation results for the process of homogeneous formation of nanosized cavities in a single-component amorphous metallic alloy. To identify cavities of various shapes and sizes, an original method has been developed, which is based on filling cavities by virtual particles (balls) of the same diameter. By means of the mean first-passage time analysis, it was shown that the cavity formation in an amorphous metallic melt is the activation-type process. This process can be described in terms of the classical nucleation theory, which is usually applied to the case of first order phase transitions. Activation energy, critical size and nucleation rate of cavities are calculated, the values of which are comparable with those for the case of crystal nucleation in amorphous systems.