A subset \(P \subseteq V(G)\) is called a open packing set of a graph G, if each pair of distinct vertices in P has disjoint open neighborhoods. The open packing number \(\rho _o(G)\) is the cardinality of a maximum open packing set in G. An open packing set S of a graph G is said to be k-regular if the induced subgraph \(\langle S \rangle \) is k-regular. We define a graph G as a strongly k-regular open packing graph (SkROPG) if every maximum open packing set of G induces a k-regular subgraph of G. In this article, we initiate the study of k-regular open packing set and characterize certain classes of S0ROPG and S1ROPG. Additionally, we establish necessary and sufficient conditions for the corona product of graphs to be an S0ROPG. In particular, we provide a complete characterization of all trees T with \(diam(T)\le 6\) that satisfy the S1ROPG property.