This study presents the advantages of combining three-dimensional biodegradable scaffolds with the injection bioprinting of hydrogels. This combination takes advantage of the synergic effect of the properties of the various components, namely the very favorable mechanical and structural properties of fiber scaffolds fabricated from polycaprolactone and the targeted injection of a hydrogel cell suspension with a high degree of hydrophilicity. These properties exert a very positive impact in terms of promoting inner cell proliferation and the ability to create compact tissue. The scaffolds were composed of a mixture of microfibers produced via meltblown technology that ensured both an optimal three-dimensional porous structure and sufficient mechanical properties, and electrospun nanofibers that allowed for good cell adhesion. The scaffolds were suitable for combination with injection bioprinting thanks to their mechanical properties, i.e., only one nanofibrous scaffold became deformed during the injection process. A computer numerical-control manipulator featuring a heated printhead that allowed for the exact dosing of the hydrogel cell suspension into the scaffolds was used for the injection bioprinting. The hyaluronan hydrogel created a favorable hydrophilic ambiance following the filling of the fiber structure. Preliminary in vitro testing proved the high potential of this combination with respect to the field of bone tissue engineering. The ideal structural and mechanical properties of the tested material allowed osteoblasts to proliferate into the inner structure of the sample. Further, the tests demonstrated the significant contribution of printed hydrogel-cell suspension to the cell proliferation rate. Thus, the study led to the identification of a suitable hydrogel for osteoblasts.