In the present paper, we study the properties of singular Nakano positivity of singular Hermitian metrics on holomorphic vector bundles, and establish an optimal L² extension theorem for holomorphic vector bundles with singular Hermitian metrics on weakly pseudoconvex Kähler manifolds, which is a unified version of the optimal L² extension theorems for holomorphic line bundles with singular Hermitian metrics of Guan–Zhou and Zhou–Zhu. As applications, we give a necessary condition for the holding of the equality in optimal L² extension theorem, and present singular Hermitian holomorphic vector bundle versions of some L² extension theorems with optimal estimate.