A simple one-pot method is proposed for obtaining the colloidal nanohybrid structures of silver (gold) and zinc oxide as well as nanostructures doped with zinc ions. The copolymers of maleic acid were used for the stabilization of nanoheterostructures. To characterize the preparation, UV–Vis spectroscopy, TEM, FTIR, XPS, and XRD were used. The bactericidal properties of the nanoheterostructures were studied in relation to the fungus C. albicans and the bacteria E. coli and S. aureus, used in planktonic form. In general, the samples containing nanosilver were the most active, and the preparations containing gold nanoparticles were the least active. The minimum inhibitory concentrations (MICs) of the Ag/ZnO samples, based on all copolymers, were in the ranges of 1.4–1.7 μg/mL for C. albicans, 2.9–6.8 μg/mL for E. coli, and 23–27 μg/mL for S. aureus; the MIC values of Au/ZnO samples were 472 μg/mL for S. aureus and 945 μg/mL for C. albicans and E. coli. The additional introduction of zinc cations into heterodimers had practically no effect on the antimicrobial properties of the composites. For all prepared composites and all tested microorganisms, the fractional inhibitory concentration indexes were in the range of 0.5–2.2, which indicates a close-to-additive contribution of the bioactive components in the samples used in the bactericidal process.