Orbital magnetization is known empirically to play an important role in several magnetic phenomena, suchas permanent magnetism and ferromagnetic superconductivity. Within the recently developed “modern theoryof orbital magnetization,” theoretical insight has been gained into the nature of this often neglected contributionto magnetism but is based on an underlying mean-field approximation. From this theory, a few treatments haveemerged which also take into account correlations beyond the mean-field approximation. Here, we apply thes cheme developed in a previous work [F. Aryasetiawan et al., Phys. Rev. B 93, 161104(R) (2016)] to thespin- 1/2 Haldane-Hubbard model to investigate the effect of charge fluctuations on the orbital magnetizationwithin the GW approximation. Qualitatively, we are led to distinguish between two quite different situations:(i) When the lattice potential is larger than the nearest-neighbor hopping, the correlations are found to boostthe orbital magnetization. (ii) If the nearest-neighbor hopping is instead larger than the lattice potential, thecorrelations reduce the magnetization. The boost and reduction are identified to stem from interband andintraband correlations, respectively, and the relative importance of the two varies with the strength of the latticepotential. We finally study graphene with parameters obtained from first principles.