As generalizations of separable and Frobenius algebras, separable and Frobenius monoidal Hom-algebras are introduced. They are all related to the Hom-Frobenius-separability equation (HFS-equation). We characterize these two Hom-algebraic structures by the same central element and different normalizing conditions, and the structure of these two types of monoidal Hom-algebras is studied. The Nakayama automorphisms of Frobenius monoidal Hom-algebras are considered.