A recently used material that shows environmental and technical advantages for use as an asphalt binder modifier is biochar (BC). Different biomasses can be converted into BC by pyrolysis. One agro-industrial biomass that is abundant in copious quantities is oil palm mesocarp fiber (OPMF) obtained from African palm cultivation. In the present study, the use of a BC obtained from OPMF (BC-OPMF) as a modifier of asphalt binder (AC type) to produce a hot mix asphalt (HMA) was evaluated. This type of BC has not been investigated or reported in the reference literature as a binder and/or asphalt mix modifier. Initially, AC was modified with BC in three ratios (BC/AC = 5, 10, and 15%, with respect to mass) to perform penetration, softening point, and rotational viscosity tests; rheological characterization at high and intermediate temperatures; and scanning electron microscope (SEM) visualization. Based on this experimental phase, BC/AC = 10% was chosen to manufacture the modified HMA. Resistance parameters under monotonic loading (stability—S, flow—F, S/F ratio of the Marshall test, and indirect tensile strength in dry—ITSD and wet—ITSC conditions) and cyclic loading (resilient modulus, permanent deformation, and fatigue resistance under stress-controlled conditions) were evaluated on the control HMA (AC unmodified) and the modified HMA. Additionally, the tensile strength ratio (TSR) was calculated to evaluate the resistance to moisture damage. Abrasion and raveling resistance were evaluated by performing Cantabro tests. BC-OPMF is shown to be a sustainable and promising material for modifying asphalt binders for those seeking to increase stiffness and rutting resistance in high-temperature climates, resistance to moisture damage, raveling, and fatigue without increasing the optimum asphalt binder content (OAC), changing the volumetric composition of the HMA or increasing the manufacturing and construction temperatures.