Moringa oleifera Lam. has been considered as a multipurpose tree. The studies on it focus on its variable nutritional benefits. It is growing in many regions, but information about nutritional properties of those growing in the Caribbean is missing. The present study focused on biochemical analysis of main nutritional and antioxidant properties in plant material—dried leaves and seeds—of Moringa oleifera. The composition of lipids, proteins, and vitamin E was evaluated in powdered dried leaves and seeds. Fatty acids were evaluated in oil extracted from the moringa seeds. Potential antioxidant properties of the moringa were evaluated in extract from crushed and powdered leaves, as well as from the powdered seeds. The total amounts of lipids, proteins, and vitamin E were higher in powdered seeds (31.85%, 35.13%, and 220.61 mg/kg) than in powdered leaves (12.48%, 20.54%, and 178.10 mg/kg). The main compound of fatty acids presented oleic acid (76.78%) in seeds’ oil and oleic (25.01%), palmitic (24.84%), and linolenic (24.71%) acids in leaves. Neohesperidin (126.8 mg/kg), followed by chlorogenic acid (99.96 mg/kg) and quercetin (43.44 and 21.44 mg/kg) were main phenolic compounds identified. Total phenols in powdered leaves’ extract (635.6 mg GAE/L) was higher than in powdered seeds’ extract (229.5 mg GAE/L). The activity against superoxide radical and hydroxyl radical was 92.4% and 73.1% by leaves’ powder extract and 83.6% and 60.7% by crushed-leaf extract; seed-powder extract exhibited a pro-oxidation activity (−68.4%) against superoxide radical and the lowest antioxidant effect against the hydroxyl radical (55.0%).