We establish the existence of non-constant closed geodesics on moduli spaces of SU(2) monopoles of arbitrary charge. More generally, we show that the moduli space of strongly centred monopoles of charge k, , contains a totally geodesic submanifold which can be identified with the moduli space of strongly centred 2-monopoles for even k's and with the moduli space of centred 2-monopoles for odd k's. This submanifold consists of monopoles corresponding to k collinear equally spaced particles.