We study the consequences on the neutrino oscillation parameter space, mixing angle (tan 2 ), and vacuum mass difference (Ám 2 0 ) when mass varying neutrino (MaVaN) models are assumed in a supernova environment. We consider electronic to sterile channels e ! s and " e ! " s in two-flavor scenario. In a given model of MaVaN mechanism, we induce a position-dependent effective mass difference, Ám 2 ðrÞ, where r is the distance from the supernova core, that changes the neutrino and antineutrino flavor conversion probabilities. We study the constraints on the mixing angle and vacuum mass difference coming from r-process and the SN1987A data. Our result is the appearance of a new exclusion region for very small mixing angles, tan 2 ¼ 10 À6 -10 À2 , and small vacuum mass difference, Ám 2 0 ¼ 1-20 eV 2 , due the MaVaN mechanism.