We study the consequences on the neutrino oscillation parameter space, mixing angle ($tan^2theta$) and vacuum mass difference ($Delta m^2_0$), when mass varying neutrino (MaVaN) models are assumed in a supernova environment. We consider electronic to
sterile channels $ u_e rightarrow u_s$ and $bar u_e rightarrow bar u_s$ in two-flavor scenario. In a given model of MaVaN mechanism, we induce a position-dependent effective mass difference, $Delta tilde m^2(r)$, where $r$ is the distance from the supernova core, that changes the neutrino and anti-neutrino flavour 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, $tan^2theta=10^{-6}-10^{-2}$, and small vacuum mass difference, $Delta m^2_0=~1-20$ eV$^2$, due the MaVaN mechanism.
