Abstract: The experimental search for magnetic monopole particles(1-3) has, so far, been in vain. Nevertheless, these elusive particles of magnetic charge have fuelled a rich field of theoretical study(4-10). Here, we created an approximation of a magnetic monopole in free space at the end of a long, nanoscopically thin magnetic needle(11). We experimentally demonstrate that the interaction of this approximate magnetic monopole field with a beam of electrons produces an electron vortex state, as theoretically predicted for a true magnetic monopole(3,11-18). This fundamental quantum mechanical scattering experiment is independent of the speed of the electrons and has consequences for all situations where electrons meet such monopole magnetic fields, as, for example, in solids. The set-up not only shows an attractive way to produce electron vortex states but also provides a unique insight into monopole fields and shows that electron vortices might well occur in unexplored solid-state physics situations.