  We use atmospheric neutrino data and MINOS data to constrain the MaVaN (Mass
Varying Neutrinos) mechanism. The MaVaN model was largely studied in cosmology
scenarios and comes from the coupling of the neutrinos with a neutral scalar
depending on the local matter density. For atmospheric neutrinos, this new
interaction affects the neutrino propagation inside the Earth, and as
consequence, induces modifications in their oscillation pattern. To perform
such test for a non-standard oscillation mechanism with a non-diagonal neutrino
coupling in the mass basis, we analyze the angular distribution of atmospheric
neutrino events as seen by the Super-Kamiokande experiment for the events in
the Sub-GeV and multi-GeV range and muon neutrinos (anti-neutrinos) in MINOS
experiment. From the combined analysis of these two sets of data we obtain the
best fit for $\Delta m^{2}_{32}=2.45 \times 10^{-3}$ eV$^{2}$,
$sin^{2}(\theta_{23})=0.42 $ and MaVaN parameter $\alpha_{32}=0.28$ with modest
improvement, $\Delta \chi^{2}= 1.8$, over the standard oscillation scenario.
The combination of MINOS data and Super-Kamiokande data prefers small values of
MaVaN parameter $\alpha_{32} < 0.31 $ at $90 \%$ C. L..
