We present the first search for new flavor-dependent long-range interactions (LRI) of neutrinos using publicly available 8 years of high-purity ${\nu }_{\mu }$ charged-current events from IceCube DeepCore. These interactions are mediated by ultra-light gauge bosons with masses below ${10}^{-10}$ eV, which can arise due to a new lepton-number gauge symmetry, such as $L_e-L_{\mu }$ or $L_e-L_{\tau }$. These long-range interactions induce matter potential between neutrinos and abundant electrons present in distant astrophysical sources. These LRI potentials could modify neutrino oscillation probabilities. By probing the effects of LRI on atmospheric neutrino oscillations at IceCube DeepCore, we place world-leading constraints on the coupling strength of these interactions.