We construct a spacetime whose only source of curvature is a Dirac magnetic monopole, and whose geometry inherits the structure of lines of singularities of the monopole electromagnetic potentials. The spacetime has the topology S³ x R, is stationary and asymptotically at but not asymptotically Minkowskian, with its at null infinity having the topology of S³. These mild pathologies, as acausality and string structure, allow the spacetime configuration to have a gravitational magnetic mass, which results proportional to the charge mu of the monopole. This suggests that the Dirac monopole may be the source of magnetic mass in gravitational configurations, which has no Newtonian analogue. Alsomu has the role of a NUT parameter in the metric of the spacetime, suggesting that the charge of the monopole can provide a physical realization of the NUT parameter.