The layered, air-stable van der Waals antiferromagnetic compound CrSBr exhibits pronounced coupling among its optical, electronic, and magnetic properties. As an example, exciton dynamics can be significantly influenced by lattice vibrations through exciton-phonon coupling. Using low-temperature photoluminescence spectroscopy, we demonstrate the effective coupling between excitons and phonons in nanometer-thick CrSBr. By careful analysis, we identify that the satellite peaks predominantly arise from the interaction between the exciton and an optical phonon with a frequency of 118 cm^-1 (∼14.6 meV) due to the out-of-plane vibration of Br atoms. Power-dependent and temperature-dependent photoluminescence measurements support exciton-phonon coupling and indicate a coupling between magnetic and optical properties, suggesting the possibility of carrier localization in the material. The presence of strong coupling between the exciton and the lattice may have important implications for the design of light-matter interactions in magnetic semiconductors and provide insights into the exciton dynamics in CrSBr. This highlights the potential for exploiting exciton-phonon coupling to control the optical properties of layered antiferromagnetic materials.