Several astronomical and cosmological observations confirmed that our universe is vastly composed of dark matter. When neutrinos propagate, they may interact with environmental dark matter particles, giving rise to rich phenomenology in oscillation experiments. When we consider dark matter to be a complex scalar field, the correction due to dark non-standard interaction (NSI) appears as a perturbation to the mass-squared term in the neutrino Hamiltonian. The correction for neutrinos and anti-neutrinos has the opposite sign, which introduces a CPT violation in neutrino oscillations. In this work, we have investigated the effect of dark NSI in the Deep Underground Neutrino Experiment (DUNE). The additional mixing parameters arising as a result of the dark NSI correction introduce degeneracies in the measurement of oscillation parameters. They may also act as additional sources of CP violation apart from the genuine Dirac CP phase. We have investigated the phenomenological consequences of dark NSI in neutrino oscillation and its effect on the CP violation sensitivity of the DUNE experiment.