We investigate the capability of the DUNE Near Detector (ND) to constrain Non Standard Interaction parameters (NSI) describing the production of neutrinos ($varepsilon_{alphabeta}^s$) and their detection ($varepsilon_{alphabeta}^d$). We show that the DUNE ND is able to reject a large portion of the parameter space allowed by DUNE Far Detector analyses and to set the most stringent bounds from accelerator neutrino experiments on $|varepsilon_{mu e}^{s,d}|$ for wide intervals of the related phases. We also provide simple analytic understanding of our results as well as a numerical study of their dependence on the systematic errors, showing that the DUNE ND offers a clean environment where to study source and detector NSI.