  The neutral current non-standard interactions (NSI's) of neutrino with matter
fermions while propagating through long distances inside the Earth matter can
give rise to the extra matter potentials apart from the standard MSW potential
due to the $W$-mediated interactions in matter. In this paper, we explore the
impact of flavor violating neutral current NSI parameter
$\varepsilon_{\mu\tau}$ in the oscillation of atmospheric neutrino and
antineutrino using the 50 kt magnetized ICAL detector at INO. We find that due
to non-zero $\varepsilon_{\mu\tau}$, $\nu_\mu\rightarrow\nu_\mu$ and
$\bar\nu_\mu\rightarrow\bar\nu_\mu$ transition probabilities get modified
substantially at higher energies and longer baselines, where vacuum oscillation
dominates. We estimate the sensitivity of the ICAL detector for various choices
of binning schemes and observables. The most optimistic bound on
$\varepsilon_{\mu\tau}$ that we obtain is $-0.01 < \varepsilon_{\mu\tau} < 0.01
$ at 90$\%$ C.L. using 500 kt$\cdot$yr exposure and considering $E_\mu,\,
\cos\theta_\mu,\,E'_{\rm had}$ as observables in their ranges [1, 21] GeV, [-1,
1], and [0, 25] GeV respectively. For the first time we show that the charge
identification capability of the ICAL detector is crucial to set stringent
constraints on $\varepsilon_{\mu\tau}$. We also show that when we marginalize
over $\varepsilon_{\mu\tau}$ in fit in its range of -0.1 to 0.1, the mass
hierarchy sensitivity deteriorates by 10$\%$ to 20$\%$ depending on the
analysis mode, and the precision measurements of atmospheric parameters remain
quite robust at the ICAL detector.
