Currently circulating SARS-CoV-2 variants have gained complete or significant resistance to all SARSCoV-2-neutralizing antibodies that have been used in the clinic. Such antibodies can prevent severe disease in SARS-CoV-2 exposed patients for whom vaccines may not provide optimal protection. Here, we describe single-domain antibodies (VHHs), also known as nanobodies, that can broadly neutralize SARS-CoV-2 with unusually high potency. Structural analysis revealed their binding to a unique, highly conserved, membrane proximal, quaternary epitope in the S2 subunit of the spike. Furthermore, a VHH-human IgG1 Fc fusion, efficiently expressed in Chinese hamster ovary cells as a stable antibody construct, protected hamsters against SARS-CoV-2 replication in a therapeutic setting when administered systemically at low dose. This VHH-based antibody represents a new candidate anti-COVID-19 biologic that targets the Achilles heel of the viral spike.