Adding right-handed neutrinos to the Standard Model is a natural and simple extension and is well motivated on both the theoretical and the experimental side. We extend the Standard Model by adding only one right-handed Majorana neutrino and study the sensitivity of the Near Detector of the DUNE experiment to the new physics parameters, namely the mixing parameters $|U_{e 4}|^2$ and $|U_{mu 4}|^2$ and the mass $m_N$. The study relies on searches of the products of right-handed neutrino decays, which is possible thanks to an extremely intense beam and a state-of-the-art detection technology. This type of direct test is carried out with very few assumptions and in an almost-completely model-independent way, providing thus a strong result. A background analysis is also performed, simulating the detector performance to particle identification. It is found that the existing bounds in the MeV-range can be improved by one order of magnitude in different detection channels.