The bacterial cytoskeletal protein FtsZ is a GTPase that is thought to provide mechanical constriction force via an unidentified mechanism. Purified FtsZ polymerizes into filaments with varying structures in vitro: while GTP-bound FtsZ assembles into straight or gently curved filaments, GDP-bound FtsZ forms highly curved filaments, prompting the hypothesis that a difference in the inherent curvature of FtsZ filaments provides mechanical force. However, no nucleotide-dependent structural transition of FtsZ monomers has been observed to support this force generation model. Here, we present a series of all-atom molecular dynamics simulations probing the effects of nucleotide binding on the structure of an FtsZ dimer. We found that the FtsZ-dimer structure is dependent on nucleotide-binding state. While a GTP-bound FtsZ dimer retained a firm monomer-monomer contact, a GDP-bound FtsZ dimer lost some of the monomer-monomer association, leading to a “hinge-opening” event that resulted in a more bent dimer, while leaving each monomer structure largely unaffected. We constructed models of FtsZ filaments and found that a GDP-FtsZ filament is much more curved than a GTP-FtsZ filament, with the degree of curvature matching prior experimental data. FtsZ dynamics were used to estimate the amount of force an FtsZ filament could exert when hydrolysis occurs (20–30 pN per monomer). This magnitude of force is sufficient to direct inward cell-wall growth during division, and to produce the observed degree of membrane pinching in liposomes. Taken together, our data provide molecular-scale insight on the origin of FtsZ-based constriction force, and the mechanism underlying prokaryotic cell division.