Magnetism has recently been observed in nominally nonmagnetic iron disilicide in the form of epitaxial γ-FeSi2 nanostructures on Si(111) substrate. To explore the origin of the magnetism in γ-FeSi2/Si(111) nanostructures, we performed a systematic first-principles study based on density functional theory. Several possible factors, such as epitaxial strain, free surface, interface, and edge, were examined. The calculations show that among these factors, only the edge can lead to the magnetism in γ-FeSi2/Si(111) nanostructures. It is shown that magnetism exhibits a strong dependency on the local atomic structure of the edge. Furthermore, magnetism can be enhanced by creating multiple-step edges. In addition, the results also reveal that edge orientation can have a significant effect on magnetism. These findings, thus, provide insights into a strategy to tune the magnetic properties of γ-FeSi2/Si(111) nanostructures through controlling the structure, population, and orientation of the edges.