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Abstract We find the constraints on various non-standard interactions (NSI) of neutrinos from monojet+ T searches at the Large Hadron Collider (LHC). Also, we show that the measurement of neutrino-nucleon cross-section from the observation of high energy astrophysical neutrino events at IceCube facilitates strong constraints on NSI as well. To this end, we pursue a comparative study of the prospects of LHC and IceCube in detecting NSI, also mentioning the role of low-energy experiments. We discuss the case of NSI with a new vector boson Z′ and it is found that for some range of mz ′ LHC puts more stringent bound, whereas IceCube supersedes elsewhere. We also pay special attention to the case of Z′ of mass of a few GeVs, pointing out that the IceCube constraints can surpass those from LHC and low-energy experiments. Although, for contact-type effective interactions with two neutrinos and two partons, constraints from LHC are superior.