Summary: Let \(\mathcal{G}\) denote a dihedral group, where 1 is identity element and \(T \subseteq \mathcal{G} \setminus \{1\}\). We define \(T\) as minimal if \(T\) satisfies the condition \(\langle T \rangle = \mathcal{G}\), and there is an element \(s \in T\) satisfying \(\langle T \setminus \{s, s^{-1}\} \rangle \neq \mathcal{G}\). Within this manuscript, we achieve a complete characterization of the directed strongly regular Cayley graph \(\operatorname{Cay}(\mathcal{G},T)\) of \(\mathcal{G}\), given the constraint that the subset \(T\) is minimal.