  Non-standard neutrino interactions (NSI) involved in neutrino propagation
inside Earth matter could potentially alter atmospheric neutrino fluxes. In
this work, we look at the impact of these NSI on the signal at the ICAL
detector to be built at the India-based Neutrino Observatory (INO). We show how
the sensitivity to the neutrino mass hierarchy of ICAL changes in the presence
of NSI. The mass hierarchy sensitivity is shown to be rather sensitive to the
NSI parameters $\epsilon_{e\mu}$ and $\epsilon_{e\tau}$, while the dependence
on $\epsilon_{\mu\tau}$ and $\epsilon_{\tau\tau}$ is seen to be very mild, once
the $\chi^2$ is marginalised over oscillation and NSI parameters. If the NSI
are large enough, the event spectrum at ICAL is expected to be altered and this
can be used to discover new physics. We calculate the lower limit on NSI
parameters above which ICAL could discover NSI at a given C.L. from 10 years of
data. If NSI were too small, the null signal at ICAL can constrain the NSI
parameters. We give upper limits on the NSI parameters at any given C.L. that
one is expected to put from 10 years of running of ICAL. Finally, we give C.L.
contours in the NSI parameter space that is expected to be still allowed from
10 years of running of the experiment.
