In this work, we present an effective process easily adapted in industrial environments for the development of multifunctional nanocomposites for material extrusion (MEX) 3D printing (3DP). The literature is still very limited in this field, although the interest in such materials is constantly increasing. Nanocomposites with binary inclusions were prepared and investigated in this study. Polylactic acid (PLA) was used as the matrix material, and cuprous oxide (Cu2O) and cellulose nanofibers (CNF) were used as nanoadditives introduced in the matrix material to enhance the mechanical properties and induce antibacterial performance. Specimens were built according to international standards with a thermomechanical process. Tensile, flexural, impact, and microhardness tests were conducted. The effect on the thermal properties of the matrix material was investigated through thermogravimetric analysis, and Raman spectroscopic analysis was conducted. The morphological characteristics were evaluated with atomic force microscopy (AFM), scanning electron microscopy (SEM), and energy-dispersive X-ray (EDS) analyses. The antibacterial performance of the prepared nanomaterials was studied against Staphylococcus aureus (S. aureus) and Escherichia coli (E. coli) bacteria, with a screening agar well diffusion method. All nanocomposites prepared exhibited biocidal properties against the bacteria tested. The tested PLA/1.0 CNF/0.5 Cu2O material had 51.1% higher tensile strength and 35.9% higher flexural strength than the pure PLA material.