Plant extracts are a phytochemically-rich alternative to antibiotic and synthetic feed additives, with high systemic bioactivity in animals. The present study aimed to evaluate the effect of a hydroalcoholic extract of custard apple (Annona squamosa) leaf (ASLE) on the growth, hematobiochemical parameters, digestive enzyme activities, redox status, nonspecific immune response, and cold and bacterial infection tolerance in Nile tilapia (Oreochromis niloticus). A total of 300 Nile tilapia fingerlings (11.87 ± 0.48 g) were fed ASLE-supplemented diets at increasing levels of 0, 5, 10, 15, and 20 g/kg for 60 days. At the end of the feeding period, the fish were experimentally challenged with cold water stress or Aeromonas sobria, and mortalities were recorded for 10 days. The results revealed that the growth performance and feed conversion ratio were significantly improved with an increasing level of ASLE supplementation. The hematologic profile and hepato-renal functions were retained within a healthy range in the various groups supplemented with an ASLE diet. Antioxidant status was significantly improved in the serum of fish fed ASLE-supplemented diets, in terms of superoxide dismutase (SOD), catalase (CAT) activities, reduced glutathione, and total antioxidant capacity. Meanwhile, the myeloperoxidase (MPO) and malondialdehyde (MDA) levels decreased significantly. Similarly, there was a noticeable improvement in the hepatic CAT and SOD activities and a reduction of hepatic MDA. Marked improvements in lysozyme activity, nitric oxide production, complement3 level, and phagocytic activity were recorded in groups fed ASLE-supplemented diets, which peaked with the 20 g ASLE/kg diet. Moreover, the serum glucose and cortisol levels significantly declined in groups fed ASLE at levels of 15–20 g/kg compared to the other groups. Supplementation with ASLE increased the activities of protease, lipase, and α-amylase. ASLE supplementation at a concentration of 10–20 g/kg diet enhanced the resistance of Nile tilapia to A. sobria infection. According to this study, ASLE supplementation enhanced the antioxidant balance, non-specific immune response, physiological status, resistance against infection, and growth performance of Nile tilapia at supplementation levels of 10–20 g/kg diet.