This study investigates the effects of pineapple by-products on feed preservation during storage at two different temperatures (25 °C and 4 °C) and on European sea bass (Dicentrarchus labrax) stress resistance. Four isoproteic, isolipidic, and isoenergetic diets were manufactured: CTRL—negative control, commercial diet without added antioxidants; VITE—positive control, CTRL diet with 100 mg kg−1 of vitamin E; and P2 and S2—VITE diet with 2% pineapple peel or stem flour, respectively. The fish (13.5 ± 0.8 g) were split into four replicate groups per diet and fed ad libitum for 12 weeks, after which they were subjected to a stress challenge of air exposure (1 min) followed by confinement (5 min, 100 kg m−3). Despite storage time lowering the antioxidant properties of all diets, P2 and S2 showed increased antioxidant capacity (DPPH•, ABTS•+, and ORAC) before and after storage. The diets were well accepted by the fish, and the VITE-fed fish showed significantly lower lipid peroxidation values in the liver and muscle compared to all remaining diets. However, pineapple by-product inclusion did not result in increased fish stress resistance. Further optimization is required for the successful use of pineapple by-products as natural antioxidants in aquafeeds.