Synthetic cationic polymer-mediated synthesis of silver nanoparticles and selective antimicrobial activity of the same were demonstrated. Polyethyleneimine (PEI)-coated silver nanoparticles showed antimicrobial activity against Acinetobacter baumannii as a function of the polymeric molecular weight (MW) of PEI. Silver nanoparticles were coated with PEI of three different MWs: Ag-NP-1 with PEI exhibiting a MW of 750,000, Ag-NP-2 with PEI exhibiting a MW of 1300, and Ag-NP-3 with PEI exhibiting a MW of 60,000. These nanoparticles showed a particle size distribution of 4–20 nm. The nanoparticles exhibited potent antimicrobial activity against A. baumannii, with the minimum inhibitory concentration of Ag-NP-1, Ag-NP-2, and Ag-NP-3 on the order of 5, 10, and 5 μg/mL, respectively, and minimum bactericidal concentration of Ag-NP-1, Ag-NP-2, and Ag-NP-3 on the order of 10, 20, and 10 μg/mL, respectively. Fluorescence imaging of Ag-NPs revealed selective transfusion of Ag-NPs across the cell membrane as a function of the polymeric MW; differential interaction of the cytoplasmic proteins during antimicrobial activity was observed.