Pancreatic cancer affects many people and is quite aggressive. Metallic nanoparticles may be an alternative treatment for this disease. In this work, the antiproliferative activity of biosynthesized silver nanoparticles was evaluated. Stenocereus queretaroensis peel extract was used as a reducing agent for nanoparticle synthesis; the characterization was carried out using spectroscopic techniques, X-ray diffraction, and microscopy. The antiproliferative effect was evaluated in the MIA PaCa-2 pancreatic tumoral cell line, and a molecular docking test was run with the STAT3 protein. The results obtained show that it was possible to synthesize silver nanoparticles from the plant extract, which was confirmed through characterization studies. The average size of the nanoparticles was measured to be 48.8 nm, and they predominantly exhibited a spherical shape. The antiproliferative effect was demonstrated in the pancreatic cell line, with an IC50 value of 15.66 µg/mL. The molecular docking analysis predicted a strong interaction with the STAT3 protein, with a binding energy value of −6.47 obtained. With these results, it is concluded that biosynthesized silver nanoparticles inhibit pancreatic tumor cell growth and may represent an innovative cancer treatment.