Pancreatic cancer is a type of cancer that is aggressive and has a high mortality rate with a five-year survival rate. The primary treatment option commonly used today is chemotherapy, which has very severe side effects. Considering all these side effects, the search for a new treatment for pancreatic cancer is extremely important. In this study, the cytotoxicity effect of silver sulfide nanoparticles (Ag<inf>2</inf>S NPs) synthesized with sweet cherry (Prunus avium L.), gemcitabine (GEM), a chemotherapy drug, and their combination (Ag<inf>2</inf>S NPs—GEM) on PANC-1 cancer cell lines was evaluated by MTT method. Additionally, the interaction of Ag<inf>2</inf>S NPs, GEM, and their combination with DNA was examined by conducting agarose gel electrophoresis. Also, interactions of Ag<inf>2</inf>S NPs, GEM, and their combination (Ag<inf>2</inf>S NPs—GEM) with key enzymes involved in nucleotide synthesis and DNA replication were investigated using molecular docking. The cytotoxicity results in PANC-1 cancer cell lines indicated that the most effective incubation period for Ag<inf>2</inf>S NPs was 24 hours (IC<inf>50</inf>: 75.77 µg/mL), while the most effective results for gemcitabine were obtained at 72 hours (IC<inf>50</inf>: 32.77 µg/mL). The combined application of Ag<inf>2</inf>S NPs and GEM produced significantly more effective results compared to monotherapy (IC<inf>50</inf>: 18.97 µg/mL in 72 h). DNA cleavage study showed that both Ag<inf>2</inf>S NPs and GEM bind to DNA, especially Ag<inf>2</inf>S NPs has affinity for G-G bases. The Ag<inf>2</inf>S NPs—GEM combination showed highly favorable binding affinities compared to Ag<inf>2</inf>S and metabolites of GEM, particularly against thymidylate synthase (ΔG = −6.52 kcal/mol) and DNA polymerase alpha catalytic core (ΔG = −6.65 kcal/mol), correlating with its potent cytotoxicity in PANC-1 cells. Additionally, docking simulations with B-DNA revealed that Ag<inf>2</inf>S NPs—GEM exhibits the strongest DNA-binding affinity (ΔG = −7.93 kcal/mol), acting as an effective DNA binder that may enhance cytotoxicity in PANC-1 cells.