Abiotic stresses, including drought and salinity, negatively affect plant development and physiology at molecular and metabolic levels. Sucrose transport, mediating distribution of photosynthates in plant, is a key physiological process impacted by drought and salinity stresses, as sucrose is a prime energy and signaling molecule as well as an osmolyte. Therefore, understanding the effects of abiotic stresses on sucrose transport and transporters, and underlying genetic and molecular mechanisms, is imperative to maintain sugar homeostasis in plants under stress. Here, we investigated the effects of drought and salinity stresses on sucrose transport and distribution, and on expression levels of genes encoding Sugars Will Eventually be Exported Transporters (SWEETs), along with a potential transcription factor regulating SWEET expression in rice. We observed that drought and salinity stresses increased the sucrose content in leaf and root tissues and in phloem sap of rice indica varieties. Expression analyses of SWEET genes and histochemical analysis of β-glucuronidase-reporter transgenic plants suggested that OsSWEET13 and OsSWEET15 are major SWEET transporters regulating the sucrose transport and levels in response to the abiotic stresses. Transactivation analyses showed that an abscisic acid (ABA)-responsive transcription factor OsbZIP72 directly binds to the promoters of OsSWEET13 and OsSWEET15 and activates their expression. Taken together, the results showed that the higher expressions of OsSWEET13 and OsSWEET15 genes, induced by binding of an ABA-responsive transcription factor OsbZIP72 to the promoters, potentially modulate sucrose transport and distribution in response to the abiotic stresses. The mechanism could possibly be targeted for maintaining sugar homeostasis in rice under drought and salinity stresses.