An eco-friendly plant-mediated approach was employed for the synthesis of green zinc oxide nanoparticles (ZnO NPs) and silver-doped zinc oxide nanoparticles (Ag-doped ZnO NPs), using Artemisia Absinthium leaf extract as a reducing and capping agent. Pure ZnO NPs were also synthesized without the leaf extract, and a comparative study between them was conducted. The nanoparticles (NPs) were characterized using Fourier transform infrared (FTIR) spectroscopy, X-ray diffraction (XRD), morphological scanning electron microscopy/energy dispersive spectrum (SEM/EDX), and surface area (BET) analysis, and antioxidant and antibacterial activity measurements were conducted. The FTIR analysis showed the absorption peak of the Zn–O bond between 400 and 450 cm−1. The XRD analysis revealed that the ZnO NPs had a hexagonal wurtzite structure with a decrease in particle size from 36.32 to 27.40 to 25.13 nm, and an increase in the BET from 4.003 to 6.032 to 12.151 m2/g for the pure, green, and Ag-doped ZnO NPs, respectively. The field emission scanning electron microscopy (FESEM) imaging revealed the presence of the ZnO NPs. The EDX results showed the zinc and oxygen composition exhibited strong energy signals of 71.28% and 18.12% for zinc and oxygen, respectively. The various characterization techniques used confirmed the formation of the ZnO NPs. The free radical scavenging activities (RSِA%) measured using the 1,1-diphenyl-2-picrylhydrazyl free radical (DPPH) assay at different concentrations and times for the pure, green, and Ag-doped ZnO NPs, and ascorbic acid were 25.50, 29.27, 28.56, and 56.7, respectively. The antibacterial activity of the synthesized samples was tested against three types of bacteria, Staphylococcus aureus ATCC 6538, Bacillus subtilis ATCC 6633, and Pseudomonas aeruginosa ATCC 9027, at different levels (5, 10, 20, and 30 µL), using the hole plate diffusion method. The Ag/ZnO NPs showed more enhanced antibacterial activity than the green ZnO NPs, whereas the pure ZnO NPs showed no antibacterial activity under the same conditions. Comparatively, the antibacterial activity of the Ag-doped ZnO NPs against the test bacteria was found to be higher than that of a commercial gentamycin antibiotic. Ultimately, the present investigation has clearly shown that the differences in the ZnO NPs’ sizes and surface-area-to-volume ratios are responsible for their stronger antibacterial activity.