Leaf senescence reduces the photosynthetic capacity of leaves, thus significantly affecting the growth, development, and yield formation of cotton. Melatonin (MT) is a multipotent substance proven to delay leaf senescence. However, its potential mechanism in delaying leaf senescence induced by abiotic stress remains unclear. This study aimed to explore the effect of MT on delaying drought-induced leaf senescence in cotton seedlings and to clarify its morphological and physiological mechanisms. Drought stress upregulated the leaf senescence marker genes, destroyed the photosystem, and led to excessive accumulation of reactive oxygen species (ROS, e.g., H2O2 and O2−), thus accelerating leaf senescence. However, leaf senescence was significantly delayed when 100 μM MT was sprayed on the leaves of the cotton seedlings. The delay was embodied by the increased chlorophyll content, photosynthetic capacity, and antioxidant enzyme activities, as well as decreased H2O2, O2−, and abscisic acid (ABA) contents by 34.44%, 37.68%, and 29.32%, respectively. MT significantly down-regulated chlorophyll degradation-related genes and senescence marker genes (GhNAC12 and GhWRKY27/71). In addition, MT reduced the chloroplast damage caused by drought-induced leaf senescence and maintained the integrity of the chloroplast lamellae structure under drought stress. The findings of this study collectively suggest that MT can effectively enhance the antioxidant enzyme system, improve photosynthetic efficiency, reduce chlorophyll degradation and ROS accumulation, and inhibit ABA synthesis, thereby delaying drought-induced leaf senescence in cotton.