Three-dimensional (3D) printing technology has become a popular tool to produce complex structures. It has great potential in the regenerative medicine field to produce customizable and reproducible scaffolds with high control of dimensions and porosity. This study was focused on the investigation of new biocompatible and biodegradable 3D-printed scaffolds with suitable mechanical properties to assist tendon and ligament regeneration. Polylactic acid (PLA) scaffolds were reinforced with 0.5 wt.% of functionalized graphite nanoplatelets decorated with silver nanoparticles ((f-EG)+Ag). The functionalization of graphene was carried out to strengthen the interface with the polymer. (f-EG)+Ag exhibited antibacterial properties against Staphylococcus aureus (S. aureus) and Escherichia coli (E. coli), an important feature for the healing process and prevention of bacterial infections. The scaffolds’ structure, biodegradation, and mechanical properties were assessed to confirm their suitability for tendon and ligamentregeneration. All scaffolds exhibited surface nanoroughness created during printing, which was increased by the filler presence. The wet state dynamic mechanical analysis proved that the incorporation of reinforcement led to an increase in the storage modulus, compared with neat PLA. The cytotoxicity assays using L929 fibroblasts showed that the scaffolds were biocompatible. The PLA+[(f-EG)+Ag] scaffolds were also loaded with human tendon-derived cells and showed their capability to maintain the tenogenic commitment with an increase in the gene expression of specific tendon/ligament-related markers. The results demonstrate the potential application of these new 3D-printed nanocomposite scaffolds for tendon and ligament regeneration.