Sucrose is the main photosynthesis product of plants and the fundamental carbon skeleton monomer and energy supply for seed formation and development. Drought stress induces decreased photosynthetic carbon assimilation capacity, and seriously affects seed weight in soybean. However, little is known about the relationship between decreases in soybean seed yield and disruption of sucrose metabolism and transport balance in leaves and seeds during the reproductive stages of crop growth. Three soybean cultivars with similar growth periods, “Shennong17”, “Shennong8”, and “Shennong12”, were subjected to drought stress during reproductive growth for 45 days. Drought stress significantly reduced leaf photosynthetic rate, shoot biomass, and seed weight by 63.93, 33.53, and 41.65%, respectively. Drought stress increased soluble sugar contents, the activities of sucrose phosphate synthase, sucrose synthase, and acid invertase enzymes, and up-regulated the expression levels of GmSPS1, GmSuSy2, and GmA-INV, but decreased starch content by 15.13% in leaves. Drought stress decreased the contents of starch, fructose, and glucose in seeds during the late seed filling stages, while it induced sucrose accumulation, which resulted in a decreased hexose-to-sucrose ratio. In developing seeds, the activities of sucrose synthesis and degradation enzymes, the expression levels of genes related to metabolism, and the expression levels of sucrose transporter genes were enhanced during early seed development under drought stress; however, under prolonged drought stress, all of them decreased. These results demonstrated that drought stress enhances the capacity for unloading sucrose into seeds and activated sucrose metabolism during early seed development. At the middle and late seed filling stages, sucrose flow from leaves to seeds was diminished, and the balance of sucrose metabolism was impaired in seeds, resulting in seed mass reduction. The different regulation strategies in sucrose allocation, metabolism, and transport during different seed development stages may be one of the physiological mechanisms for soybean plants to resist drought stress.