The rodent-borne hantavirus Puumala virus (PUUV) and related agents cause hemorrhagic fever with renal syndrome (HFRS) in humans. Other hantaviruses, including Andes virus (ANDV) and Sin Nombre virus, cause a distinct zoonotic disease, hantavirus cardiopulmonary syndrome (HCPS). Although these infections are severe and have substantial case fatality rates, no FDA-approved hantavirus countermeasures are available. Recent work suggests that monoclonal antibodies may have therapeutic utility. We describe here the isolation of human neutralizing antibodies (nAbs) against tetrameric Gn/Gc glycoprotein spikes from PUUV-experienced donors. We define a dominant class of nAbs recognizing the "capping loop" of Gn that masks the hydrophobic fusion loops in Gc. A subset of nAbs in this class, including ADI-42898, bound Gn/Gc complexes but not Gn alone, strongly suggesting that they recognize a quaternary epitope encompassing both Gn and Gc. ADI-42898 blocked the cell entry of seven HCPS- and HFRS-associated hantaviruses, and single doses of this nAb could protect Syrian hamsters and bank voles challenged with the highly virulent HCPS-causing ANDV and HFRS-causing PUUV, respectively. ADI-42898 is a promising candidate for clinical development as a countermeasure for both HCPS and HFRS, and its mode of Gn/Gc recognition informs the development of broadly protective hantavirus vaccines.