Quantum interference is a coherent quantum phenomenon that takes place in confined geometries. Using spin-polarized scanning tunneling microscopy, we found that quantum interference of electrons causes spatial modulation of spin polarization within a single magnetic nanostructure. We observed changes in both the sign and magnitude of the spin polarization on a subnanometer scale. A comparison of our experimental results with ab initio calculations shows that at a given energy, the modulation of the spin polarization can be ascribed to the difference between the spatially modulated local density of states of the majority spin and the nonmodulated minority spin contribution.