The growing emphasis on sustainable and lightweight engineering materials has driven increasing interest in natural fiber–reinforced composites. Among potential fiber sources, Moringa oleifera (drumstick) offers high cellulose content and ease of extraction yet remains underexplored in composite reinforcement applications. This study aimed to fabricate and characterize a drumstick fiber–reinforced epoxy composite, evaluating its tensile, flexural, and impact properties, and comparing its mechanical performance with that of a conventional natural fiber (coir–epoxy) composite. Fibers were extracted from drumstick pods through water retting, cleaned, dried, and hand-woven into plate-shaped mats. Using the hand lay-up technique, four-layer laminates were fabricated with epoxy resin (LY556) and hardener (HY951) in a 10:1 ratio. Standardized ASTM specimens were prepared for tensile (D638), flexural (D7264), and Charpy impact (D5628) tests, performed using universal testing and impact machines. The composite exhibited tensile strength of 11.77 MPa, flexural strength of 41.03 MPa, and impact strength of 8.33 kJ/m², with elastic moduli of 1.21 GPa (tensile) and 25.7 MPa (flexural). Compared with coir fiber composites, the drumstick–epoxy system showed lower tensile and impact performance but notably higher flexural strength, indicating strong bending resistance but limited ductility. These findings suggest that drumstick fibers form adequate adhesion with the epoxy matrix but require chemical surface modification or fiber hybridization to enhance interfacial bonding and tensile properties. The composite’s stiffness and biodegradability make it suitable for non-load-bearing components, interior panels, and lightweight applications where flexural stresses dominate.