We investigate non-standard interactions of neutrinos with atomic nuclei through excitations of leptoquarks. A leptoquark term in the Lagrangian admits the possibility that neutrinos interact with gluons. The current lower limits on the leptoquark masses are of the order of 1 TeV depending on the leptoquark quantum numbers and couplings. Such heavy states can be produced in ultra-high energy cosmic neutrino scattering processes. The four-momentum transfer squared and the Bjorken variable simultaneously probed in these processes may reach values kinematically inaccessible at present collider experiments. We study the impact of the gluon density in a nucleus on the cross section for the neutrino-induced leptoquark production. We show that taking into account the nuclear parton distributions shifts the production threshold to significantly lower neutrino energies. As a particular case we consider the interaction with oxygen, which is abundant in water targets used in neutrino detection experiments.