Nosocomial bacterial and fungal infections are one of the main causes of high morbidity and mortality worldwide, owing to the high prevalence of multidrug-resistant microbial strains. Hence, the study aims to synthesize, characterize, and investigate the antifungal and antibacterial activity of silver nanoparticles (AgNPs) fabricated using Camellia sinensis leaves against nosocomial pathogens. The biogenic AgNPs revealed a small particle diameter of 35.761 ± 3.18 nm based on transmission electron microscope (TEM) graphs and a negative surface charge of −14.1 mV, revealing the repulsive forces between nanoparticles, which in turn indicated their colloidal stability. The disk diffusion assay confirmed that Escherichia coli was the most susceptible bacterial strain to the biogenic AgNPs (200 g/disk), while the lowest sensitive strain was found to be the Acinetobacter baumannii strain with relative inhibition zones of 36.14 ± 0.67 and 21.04 ± 0.19 mm, respectively. On the other hand, the biogenic AgNPs (200 µg/disk) exposed antifungal efficacy against Candida albicans strain with a relative inhibition zone of 18.16 ± 0.14 mm in diameter. The biogenic AgNPs exposed synergistic activity with both tigecycline and clotrimazole against A. baumannii and C. albicans, respectively. In conclusion, the biogenic AgNPs demonstrated distinct physicochemical properties and potential synergistic bioactivity with tigecycline, linezolid, and clotrimazole against gram-negative, gram-positive, and fungal strains, respectively. This is paving the way for the development of effective antimicrobial combinations for the effective management of nosocomial pathogens in intensive care units (ICUs) and health care settings.