Caused by pathogenic microorganisms, infectious diseases are known to cause high mortality rates, severe burdens of disability, and serious worldwide aftermaths. Drug-resistant pathogens have reduced the efficacy of available therapies against these diseases, thus accentuating the need to search for effective antimicrobials. Medicinal plants have served as starting material for the preparation of a number of antimicrobial agents. To this end, the present study highlights the green synthesis of Cocos nucifera-based nanomaterials and evaluation of the mechanistic basis of their antimicrobial action. Accordingly, Cocos nucifera extract was used for the reduction of silver nitrate solution to afford silver nanoparticles. These entities were further incorporated onto sulfuric-acid-based activated carbons to generate the nanocomposites. The antimicrobial activity of the as-prepared nanomaterials was evaluated using the broth microdilution method, while the antioxidant activity was assessed through standard methods. The cytotoxicity of potent nanomaterials was assessed on Vero cells by the spectrophotometric method. As a result, nanoparticles were successfully synthesized, as evidenced by the ultraviolet–visible spectroscopy analysis that revealed an intense absorption spectrum at 433 nm. Fourier Transform Infrared Spectroscopy presented the functional group moieties involved as a capping and reducing agent in the synthesis of the nanomaterials. The incubation of nanomaterials with selected bacterial and fungal strains has led to significant inhibitory effects of these pathogens with minimum inhibitory concentrations ranging from 7.813 to 250 μg/mL. In antioxidant assays, the nanocomposites presented scavenging activities comparable to those of ascorbic acid. Cytotoxicity experiment revealed no toxic effects on Vero cells (range of selectivity indices: from >4 to >128). These results provide evidence of the implication of Cocos nucifera-based nanomaterials in targeting bacterial or fungal systems that mediate free-radical damage or by inhibiting the oxidative damage caused by selected bacteria and fungi, the most susceptible being Escherichia coli and Candida albicans, respectively.