The equivalence principle is a fundamental assumption of General Relativity. However, in several quantum gravity scenarios, small violations of thisprinciple (VEP) is expected. For this reason, it is important to test this principle and obtain statistical limits on its violation, in order to possibly discardsome scenarios. One way to constrain this violation is analyzing the flavor oscillation pattern of high-energy atmospheric neutrinos, generated by cosmicrays. The standard oscillation of neutrino s flavor crossing the Earth becomesnegligible at high energies, while the oscillation induced by VEP becomes increasingly prominent in this range of energy. In this work, we use a minimalisticapproach about the VEP, in which it would occur because of different valuesof gravitational constants for each neutrino mass eigenstate, parameterized asGi ≡ γiG where G is the gravitational constant, and we derive limits on theparameters Phi Deltagamma_21 and Phi Deltagamma_21 in the (Phi Deltagamma_21 , Phi Deltagamma_31) plane, where Phi is thegravitational potential. To this end, muon-tracks events generated from theinteraction of atmospheric neutrinos with the rock or ice, collected for oneyear by IceCube in its complete form (IC-86), were used. The detected muonshave energies between 400 GeV and 20 TeV, and the collected data has beencompared with the values expected by the best models of atmospheric muonneutrino production.