The recent discovery that van der Waals-bonded magnetic materials retain long range magnetic ordering down to a single layer stimulates a thorough Raman spectroscopic study of one such material, FePS₃, a large spin (S = 2) Mott insulator where the Fe atoms form a honeycomb lattice. Bulk FePS₃ was shown to be a quasi-2D Ising antiferromagnet, with additional features in the Raman spectra emerging below the Néel temperature (T_N ≈120 K). Using temperature- and magnetic field-dependent Raman spectroscopy as an optical probe of magnetic structure, we demonstrate that one of these Raman-active modes below T_N is a magnon with a frequency of ≈3.7 THz (≈122 cm^-1). Contrary to previous work, which interpreted this feature as a phonon, our Raman data shows the expected frequency shifting and splitting of the magnon as a function of temperature and magnetic field, respectively, with a g-factor ≈ 2. Furthermore, we compare our spectra with predictions from density functional theory to discuss the origin and anomalous temperature dependence of additional low-frequency Raman-active modes.