In this study, we report the green synthesis of silver nanoparticles (AgNPs) from Morus alba or white mulberry leaf extract (MLE) and assess their antibacterial and anticancer potential. The GC–MS analysis of MLE confirmed the existence of phenolic compounds, serving as reducing, capping, and stabilizing agents in the biosynthesis of AgNPs. The MLE-AgNPs were spherical, with an average particle size of 20–44.5 nm and a face-centered cubic structure. EDX spectra confirmed the formation of AgNPs, and a negative zeta potential value (−14.5 mV) suggested their physicochemical stability. Excellent antibacterial activity was demonstrated by MLE-AgNPs against Acinetobacter baumannii strains with a MIC of 2 μg/mL, while good activity was observed against other Gram-negative (Escherichia coli and Salmonella typhimurium) and Gram-positive (Bacillus subtilis and Staphylococcus aureus) bacteria with a MIC of 32 μg/mL. In vitro cytotoxic effects on MCF-7 (human breast cancer cells) and MCF-10A (normal human mammary epithelial cells) were investigated by the MTT assay. The half-maximal inhibitory concentrations (IC50) against MCF-7 cells were 18 and 33 μg/mL for MLE-AgNPs and MLE, respectively, with no effect on normal MCF-10A cells. Altogether, the results support the high antibacterial and anticancer potential of biosynthesized AgNPs by white mulberry leaf extract.