Experimentally observed sharp luminescence lines from hot free-exciton recombination in high-purity 6H- and 4H-SiC are presented. The phenomenon is explained in terms of inhibition of the exciton-phonon scattering, prohibited for excitons created resonantly near the bottom of the lowest exciton band at low temperatures. This gives rise to the hot, sharp luminescence. The model is in agreement with the observed quenching of the hot luminescence at higher temperatures (>5 K) and in more highly doped samples, as well as with the dispersion of the exciton band obtained from the measured electron and hole effective masses.