The Monoceros ring is a collection of stars in nearly circular orbits at roughly 18 kpc from the Galactic Centre. It may have originated (i) as the response of the disc to perturbations excited by satellite companions or (ii) from the tidal debris of a disrupted dwarf galaxy. The metallicity of Monoceros stars differs from that of disc stars at comparable Galactocentric distances, an observation that disfavours the first scenario. On the other hand, circular orbits are difficult to accommodate in the tidal-disruption scenario, since it requires a satellite which at the time of disruption was itself in a nearly circular orbit. Such satellite could not have formed at the location of the ring and, given its low mass, dynamical friction is unlikely to have played a major role in its orbital evolution. We search cosmological simulations for low-mass satellites in nearly circular orbits and find that they result, almost invariably, from orbital changes induced by collisions with more massive satellites: the radius of the circular orbit thus traces the galactocentric distance of the collision. Interestingly, the Sagittarius dwarf, one of the most luminous satellites of the Milky Way, is in a polar orbit that crosses the Galactic plane at roughly the same Galactocentric distance as Monoceros. We use idealized simulations to demonstrate that an encounter with Sagittarius might well have led to the circularization and subsequent tidal demise of the progenitor of the Monoceros ring.