Metallic nanoparticles with virucidal properties dispersed in a polymeric matrix have gained prominence in the scientific community as a rapid and effective alternative that employs the additive manufacturing (AM) or 3D printing method. This study aims to produce filaments for 3D printing using polymer nanocomposites based on polylactic acid (PLA) and copper nanoparticles (CuNPs) in different proportions. The virucidal activity of various proportions of nanoparticles in PLA was investigated. The composites were produced following a mixture design (DOE) with concentrations ranging from 1% to 2% copper nanoparticles, which were blended with PLA using a single-screw extruder. The samples were characterized by thermogravimetry (TG), differential scanning calorimetry (DSC), tensile strength testing, and fracture analysis using scanning electron microscopy (SEM). A thermal analysis of the composites indicated that the CuNPs contributed to an increase in the degradation temperature and crystallization of the PLA. Sample S7 (1.25% of CuNPs) exhibited a 4% increase in the degradation temperature compared to pure PLA. The best tensile strength results were observed in sample S7 (1.25% of CuNPs), 30% more than sample S3 (1.33% of CuNPs) due to good material cohesion, as evidenced by microscopy analyses. Regarding virucidal analyses, most composites demonstrated virus inhibition activity.