Phonons are the quasiparticles of collective lattice excitations that may carry finite angular momenta, but commonly exhibit negligible magnetic moments. A large phonon magnetic moment enables the direct mutual control of magnetic orders and lattice motions, and could be applied to develop spin–phononic devices. In some non- and paramagnetic systems, a large phonon magnetic moment is found due to coupling with electronic excitations. However, for magnetically ordered systems, a correspondingly large moment has not yet been discovered, and the roles of many-body correlations and fluctuations in phonon magnetism remain unclear. Here we report a phonon magnetic moment that is enhanced by critical fluctuations in a polar antiferromagnet, namely, Fe2Mo3O8. Combining magneto-Raman spectroscopy and inelastic neutron scattering measurements, we show that a pair of low-lying chiral phonons carry large magnetic moments. Once the system is driven to a ferrimagnetic phase, we observe a splitting between the chiral phonons of nearly a quarter of the phonon frequency. We also observe a sixfold enhancement in the phonon magnetic moment in the vicinity of the Néel temperature. A microscopic model based on the coupling between phonons and both magnons and paramagnons accounts for the experimental observations.