Epstein-Barr virus (EBV) is a causative agent of infectious mononucleosis and is associated with 200,000 new cases of cancer and 140,000 deaths annually. Subunit vaccines against this pathogen have focused on the gp350 glycoprotein and remain unsuccessful. We isolated human antibodies recognizing the EBV fusion machinery (gH/gL and gB) from rare memory B cells. One anti-gH/gL antibody, AMMO1, potently neutralized infection of B cells and epithelial cells, the two major cell types targeted by EBV. We determined a cryo-electron microscopy reconstruction of the gH/gL-gp42-AMMO1 complex and demonstrated that AMMO1 bound to a discontinuous epitope formed by both gH and gL at the Domain-I/Domain-II interface. Integrating structural, biochemical, and infectivity data, we propose that AMMO1 inhibits fusion of the viral and cellular membranes. This work identifies a crucial epitope that may aid in the design of next-generation subunit vaccines against this major public health burden.