We perform large-scale molecular dynamics simulations to study the magnetic properties of amorphous iron under pressure. Simulations, exceeding by at least two orders of magnitude those accessible to density functional calculations, use the recently developed magnetic interatomic potential for iron. The distributions of the size of atomic magnetic moments and parameters characterizing the structure of amorphous iron, such as radial distribution functions, are calculated as a function of the applied hydrostatic stress. As the density increases, there is a reduction in the magnitude of the mean magnetic moment of individual atoms, accompanied by the transformation of an increasing proportion of atoms from a magnetic to a nonmagnetic configuration. Beyond a critical density the proportion of nonmagnetic atoms increases sharply, yet homogeneously. The local magnetic moment of an atom correlates with the local Voronoi volume via a logarithmic relation. In addition, we observe a complex dependence of the local magnetic moment on the topological arrangement of neighboring atoms.