  The mass-induced neutrino oscillation is a well established phenomenon that
is based on the unitary mixing among three light active neutrinos. Remarkable
precision on neutrino mixing parameters over the last decade or so has opened
up the prospects for testing the possible non-unitarity of the standard 3$\nu$
mixing matrix, which may arise in the seesaw extensions of the Standard Model
due to the admixture of three light active neutrinos with heavy isosinglet
neutrinos. Because of this non-unitary neutrino mixing (NUNM), the oscillation
probabilities among the three active neutrinos would be altered as compared to
the probabilities obtained assuming a unitary 3$\nu$ mixing matrix. In such a
NUNM scenario, neutrinos can experience an additional matter effect due to the
neutral current interactions with the ambient neutrons. Atmospheric neutrinos
having access to a wide range of energies and baselines can experience a
significant modifications in Earth's matter effect due to NUNM. In this paper,
for the first time, we study in detail how the NUNM parameter $\alpha_{32}$
affects the muon neutrino and antineutrino survival probabilities in a
different way. Then, we place stringent constraints on $\alpha_{32}$ in a model
independent fashion using the proposed 50 kt magnetized Iron Calorimeter (ICAL)
detector under the India-based Neutrino Observatory (INO) project, which can
efficiently detect the atmospheric $\nu_\mu$ and $\bar\nu_\mu$ separately in
the multi-GeV energy range. Further, we discuss the advantage of charge
identification capability of ICAL and the impact of uncertainties in
oscillation parameters while constraining $\alpha_{32}$. We also compare the
$\alpha_{32}$ sensitivity of ICAL with that of future long-baseline experiments
DUNE and Hyper-K in isolation and combination.
