Abstract: Minimal Dark Matter (MDM) stands as one of the simplest dark matter scenarios. In MDM models, annihilation and co-annihilation processes among the members of the MDM multiplet are usually very efficient, pushing the dark matter mass above O(10) TeV in order to reproduce the observed dark matter relic density. Motivated by this little drawback, in this paper we consider an extension of the MDM scenario by three right-handed neutrinos. Two specific choices for the MDM multiplet are studied: a fermionic SU(2)(L) quintuplet and a scalar SU(2)(L) septuplet. The lightest right-handed neutrino, with tiny Yukawa couplings, never reaches thermal equilibrium in the early universe and is produced by freeze-in. This creates a link between dark matter and neutrino physics: dark matter can be non-thermally produced by the decay of the lightest right-handed neutrino after freeze-out, allowing to lower significantly the dark matter mass. We discuss the phenomenology of the non-thermally produced MDM and, taking into account significant Sommerfeld corrections, we find that the dark matter mass must have some specific values in order not to be in conflict with the current bounds from gamma-ray observations.