Olive leaves are an immense source of antioxidant and antimicrobial bioactive constituents. This study investigated the effects of dietary incorporation of olive leaf extract (OLE) on the growth performance, hematobiochemical parameters, immune response, antioxidant defense, histopathological changes, and some growth- and immune-related genes in the common carp (Cyprinus carpio). A total of 180 fish were allocated into four groups with triplicate each. The control group received the basal diet without OLE, while the other three groups were fed a basal diet with the OLE at 0.1, 0.2, and 0.3%, respectively. The feeding study lasted for 8 weeks, then fish were challenged with Aeromonas hydrophila. The results revealed that the group supplied with the 0.1% OLE significantly exhibited a higher final body weight (FBW), weight gain (WG%), and specific growth rate (SGR) with a decreased feed conversion ratio (FCR) compared to the other groups (p < 0.05). An increase in immune response was also observed in the fish from this group, with higher lysosome activity, immunoglobulin (IgM), and respiratory burst than nonsupplemented fish, both before and after the A. hydrophila challenge (p < 0.05). Similarly, the supplementation of the 0.1% OLE also promoted the C. carpio's digestive capacity pre- and post-challenge, presenting the highest activity of protease and alkaline phosphatase (p < 0.05). In addition, this dose of the OLE enhanced fish antioxidant capacity through an increase in the activity of superoxide dismutase (SOD) and glutathione peroxidase (GPx) and decreased hepatic lipid peroxidation end products (malondialdehyde—MDA), when compared to the control group, both pre- and post-infection (p < 0.05). Concomitantly with the superior immune response and antioxidant capacity, the fish fed the 0.1% OLE revealed the highest survival rate after the challenge with A. hydrophila (p < 0.05). A significant remarkable upregulation of the hepatic sod, nrf2, and protein kinase C transcription levels was detected as a vital approach for the prevention of both oxidative stress and inflammation compared to the infected unsupplied control group (p < 0.05). Interestingly, HPLC and UPLC-ESI-MS/MS analyses recognized that oleuropein is the main constituent (20.4%) with other 45 compounds in addition to tentative identification of two new compounds, namely oleuroside-10-carboxylic acid (I) and demethyl oleuroside-10-carboxylic acid (II). These constituents may be responsible for the OLE exerted potential effects. To conclude, the OLE at a dose range of 0.66–0.83 g/kg w/w can be included in the C. carpio diet to improve the growth, antioxidant capacity, and immune response under normal health conditions along with regulating the infection-associated pro-inflammatory gene expressions, thus enhancing resistance against A. hydrophila.