In this work, we report the synthesis of copper nanoparticles (Cu NPs), employing the chemical reduction method in an aqueous medium. We used copper sulfate pentahydrate (CuSO4·5H2O) as a metallic precursor; polyethylenimine (PEI), allylamine (AAM), and 4-aminobutyric acid (AABT) as stabilizing agents; and hydrated hydrazine as a reducing agent. The characterization of the obtained nanoparticles consisted of X-ray, TEM, FTIR, and TGA analyses. Through these techniques, it was possible to detect the presence of the used stabilizing agents on the surface of the NPs. Finally, a zeta potential analysis was performed to differentiate the stability of the nanoparticles with a different type of stabilizing agent, from which it was determined that the most stable nanoparticles were the Cu NPs synthesized in the presence of the PEI/AAM mixture. The antimicrobial activity of Cu/PEI/AABT toward P. aeruginosa and S. aureus bacteria was high, inhibiting both bacteria with low contact times and copper concentrations of 50–200 ppm. The synthesis method allowed us to obtain Cu NPs free of oxides, stable to oxidation, and with high yields. The newly functionalized Cu NPs are potential candidates for antimicrobial applications.