The biological synthesis of nanoparticles has gained considerable attention in view of their excellent biocompatibility and low toxicity. We isolated and purified rhamnolipids from Pseudomonas aeruginosa strain BS-161R, and these purified rhamnolipids were used to synthesize silver nanoparticles. The purified rhamnolipids were further characterized and the structure was elucidated based on one- and two-dimensional $^1H$ and $^{13}C$ NMR, FT-IR, and HR-MS spectral data. Purified rhamnolipids in a pseudoternary system of n-heptane and water system along with n-butanol as a cosurfactant were added to the aqueous solutions of silver nitrate and sodium borohydride to form reverse micelles. When these micelles were mixed, they resulted in the rapid formation of silver nanoparticles. The synthesized nanoparticles were characterized by UV-Visible spectroscopy, transmission electron microscopy, and energy dispersive X-ray spectroscopy (EDS). The nanoparticles formed had a sharp adsorption peak at 410 nm, which is characteristic of surface plasmon resonance of the silver nanoparticles. The nanoparticles were monodispersed, with an average particle size of 15.1 nm (${sigma}={pm}5.82$ nm), and spherical in shape. The EDS analysis revealed the presence of elemental silver signal in the synthesized nanoparticles. The formed silver nanoparticles exhibited good antibiotic activity against both Grampositive and Gram-negative pathogens and Candida albicans, suggesting their broad-spectrum antimicrobial activity.