Let G denote a dihedral group, where 1 is identity element and T⊆G∖{1}. We define T as minimal if T satisfies the condition 〈T〉=G, and there is an element s∈T satisfying 〈T∖{s,s−1}〉≠G. Within this manuscript, we achieve a complete characterization of the directed strongly regular Cayley graph Cay(G,T) of G, given the constraint that the subset T is minimal. •We introduce the concept of “minimal directed strongly regular Cayley graphs,” simplifying and enhancing the investigation process.•This manuscript provides a comprehensive characterization of minimal directed strongly regular Cayley graphs over the dihedral group, marking the first contribution to this area. Indeed, the majority of known results regarding directed strongly regular graphs are constructive in nature.•The methodology presented in this paper holds applicability to numerous other non-abelian groups, including generalized dihedral groups, dicyclic groups, and beyond.