The multifunctional profile of Zn2+ has influenced its great popularity in various pharmaceutical, food, and cosmetic products. Despite the use of different inorganic and organic zinc derivatives, the search for new zinc-containing compounds with a safer skin profile still remains an open issue. The present paper describes the synthesis, structural characterization, and antibacterial activity of zinc(II) complexes with proteinogenic amino acids as potential candidates for dermatological treatments. The obtained complexes are of the general formula [Zn(AA)2], where AA represents an amino acid (L-Glu, Gly, L-His, L-Pro, L-Met, and L-Trp). Their synthesis was designed in such a way that the final bis(aminoacidate) zinc(II) complexes did not contain any counter-ions such as Cl−, NO3−, or SO42− that can cause some skin irritations. The chemical structure and composition of the compounds were identified by 1H NMR spectroscopy and elemental analysis, and four were also characterized by single-crystal X-ray diffraction. The Hirshfeld surface analysis for the Zn2+ metallic center helped to determine its coordination number and geometry for each complex. Finally, the antibacterial properties of the complexes were determined with respect to three Gram-positive strains, viz. Staphylococcus aureus ATCC 6538, Staphylococcus epidermidis ATCC 12228, and Streptococcus pyogenes ATCC 19615, and two Gram-negative bacteria, viz. Escherichia coli ATCC 25992 and Pseudomonas aeruginosa ATCC 27853, and were compared with the activity of zinc 2-pirrolidone 5-carboxylate (ZnPCA), commonly applied in dermatology. It was found that the Zn(II) complexes with methionine and glycine exhibited a higher antibacterial activity than the tested standard, and the antimicrobial properties of complex with Trp were satisfactory. The results of the antimicrobial activity examination allow us to postulate that the obtained zinc complexes might become new active substances for use in dermatological products.