Sodium alginate (SA)-based hydrogels are often employed as bioink for three-dimensional (3D) scaffold bioprinting. They offer a suitable environment for cell proliferation and differentiation during tissue regeneration and also control the release of growth factors and mesenchymal stem cell secretome, which is useful for scaffold biointegration. However, such hydrogels show poor mechanical properties, fast-release kinetics, and low biological performance, hampering their successful clinical application. In this work, silk fibroin (SF), a protein with excellent biomechanical properties frequently used for controlled drug release, was blended with SA to obtain improved bioink and scaffold properties. Firstly, we produced a printable SA solution containing SF capable of the conformational change from Silk I (random coil) to Silk II (β-sheet): this transition is a fundamental condition to improve the scaffold’s mechanical properties. Then, the SA-SF blends’ printability and shape fidelity were demonstrated, and mechanical characterization of the printed hydrogels was performed: SF significantly increased compressive elastic modulus, while no influence on tensile response was detected. Finally, the release profile of Lyosecretome—a freeze-dried formulation of MSC-secretome containing extracellular vesicles (EV)—from scaffolds was determined: SF not only dramatically slowed the EV release rate, but also modified the kinetics and mechanism release with respect to the baseline of SA hydrogel. Overall, these results lay the foundation for the development of SA-SF bioinks with modulable mechanical and EV-release properties, and their application in 3D scaffold printing.