Abstract: The existence of monopoles is a characteristic signature of Kaluza-Klein multidimensional theories. The topology of these solutions is extremely interesting. The existence of a dipole solution, which we have associated to a monopole-anti-monopole bound state, is the leitmotiv of this investigation. The dipole in its lowest energy state, which we here call also monopolium, is electromagnetically inert in free space interacting only gravitationally. Monopolium when interacting with time dependent magnetic fields acquires a time dependent induced magnetic moment and radiates. We have analyzed the most favorable astrophysical scenario for radiative monopolium and found that the amount of radiation is so small that is not detectable by conventional equipments. These findings suggest that Kaluza-Klein monopolium, if existent, would be a candidate for a primordial dark matter constituent.