The search for new bioactive substances with microbiological activity is dictated by the increasing resistance of the drugs used in clinical practice against various pathogenic microorganisms. In this respect, particular attention is paid to the modified dendrimers with biologically active substances and their metal complexes. This work describes synthesizing and characterizing a new copper complex of first-generation polypropylene imine (PPI) dendrimer, modified with 4-sulfo-1,8-naphthalimide. The new metallodendrimer [Cu(E)(NO)] has been characterized by IR and electron paramagnetic resonance (EPR) spectroscopy. Two copper ions were found to form a complex with the dendrimer ligand. Cotton fabrics were treated with the dendrimer ligand (E), its monomer structural analog (M), and metallodendrimer. The microbiological activity of the three compounds and the treated cotton fabrics with them has been tested in the dark and after light irradiation against bacterial strains: Gram-positive B. cereus and Gram-negative P. aeruginosa. The results showed that the metallodendrimer was slightly more effective than the dendrimer ligand E and monomer M, and their activity was enhanced after light irradiation. The increase in antimicrobial activity after light irradiation was due to the generation of highly reactive singlet oxygen, which damages bacteria's cell membrane, leading to their inactivation. The similar activity against both types of bacteria indicates that all three compounds can be classified as broad-spectrum antimicrobial agents. The virucidal effects of the studied compounds were also tested against human adenovirus type 5 (HAdV5) and human respiratory syncytial virus (HRSV-S2) after 30 min/60 min. The newly synthesized compounds showed no activity against HAdV-5, but the activity against HSV-2 viruses increases with the prolongation of their interaction.