We study the low-temperature magnetophotoluminescence from individual CdSe nanocrystals. Nanocrystals having a small "bright" exciton fine structure splitting (Delta_{XY}<0.5 meV) exhibit a conventional left and right circularly polarized Zeeman photoluminescence doublet in applied magnetic fields. In contrast, nanocrystals with large Delta_{XY} (>1 meV) show an anomalous magnetophotoluminescence polarization, wherein the lower-energy peak becomes circularly polarized with increasing field, while the higher-energy peak remains linearly polarized. This unusual behavior arises from strong mixing between the absorbing and emitting bright exciton levels due to strong anisotropic exchange interactions.