Electron-hole exchange interaction in semiconductor quantum dots (QDs) splits the band-edge exciton manifold into optically active ("bright") and passive ("dark") states, leading to a complicated exciton fine structure. In the present work, we resolve by atomistic million-atom many-body pseudopotential calculations the exciton fine structure in colloidal polar and nonpolar zinc sulfide (ZnS) nanorods (NRs). We explore that polar NRs with high symmetry exhibit vanishing fine structure splitting (FSS), and are therefore ideal sources of entangled photon pairs. In contrast, nonpolar NRs grown along [Formula: see text] and [Formula: see text] directions with reduced symmetries have significant FSS, which can even reach up to a few mili electron volts. However, such large FSS can be effectively minimized to a few micro electron volts, or even less, by a simple morphology control.