We simultaneously investigate source, detector and matter non-standard neutrino interactions at the proposed DUNE experiment. Our analysis is performed using a Markov Chain Monte Carlo exploring the full parameter space. We find that the sensitivity of DUNE to the standard oscillation parameters is worsened due to the presence of non-standard neutrino interactions. In particular, there are degenerate solutions in the leptonic mixing angle θ23 and the Dirac CP-violating phase δ. We also compute the expected sensitivities at DUNE to the non-standard interaction parameters. We find that the sensitivities to the matter non-standard interaction parameters are substantially stronger than the current bounds (up to a factor of about 15). Furthermore, we discuss correlations between the source/detector and matter non-standard interaction parameters and find a degenerate solution in θ23. Finally, we explore the effect of statistics on our results.