In this paper we study the singular set of Dirichlet-minimizing Q-valued maps from R m into a smooth compact manifold N without boundary. Similarly to what happens in the case of single valued minimizing harmonic maps, we show that this set is always (m − 3)-rectifiable with uniform Minkowski bounds. Moreover, as opposed to the single valued case, we prove that the target N being non-positively curved but not simply connected does not imply continuity of the map.