The photoluminescence in CdMnTe (with x=0.15 and 0.35) was carefully studied and clear evidence for the exciton localization due to magnetic polaron (EMP) formation was presented. It was revealed that the EMP localization induced striking features on the luminescence lines; peak positions, FWHM and intensities. The heavy hole and light hole exciton magnetic polaron stability under the magnetic field was demonstrated distinctly by the polarization measurements.