In a minimal extension of the Standard Model with abelian $U(1)'$, there exists a flavor-dependent long-range leptonic force mediated by an ultralight and neutral gauge boson $Z'$ associated with $L_\mu -L_\tau$ symmetry. We study the impacts of such long-range force in the oscillation of atmospheric neutrinos assuming $Z-Z'$ mixing. We show that the proposed atmospheric neutrino detector ICAL will be able to put tight constraints on such long-range force due to its capabilities of detecting neutrino and antineutrino separately with wide ranges of energies and baselines. The expected upper limit on the parameter of this long-range force at $3\sigma$ is $2.82\times 10^{-51}$ using 500 kton$\cdot$year exposure of ICAL. }