Immune recognition of protein antigens relies on the combined interaction of multiple antibody loops, which provide a fairly large footprint and constrain the size and shape of protein surfaces that can be targeted. Single protein loops can mediate extremely high-affinity binding, but it is unclear whether such a mechanism is available to antibodies. Here we report the isolation and characterization of an antibody called C05, which neutralizes strains from multiple subtypes of influenza A virus, including H1, H2 and H3. X-ray and electron microscopy structures show that C05 recognizes conserved elements of the receptor-binding site on the haemagglutinin surface glycoprotein. Recognition of the haemagglutinin receptor-binding site is dominated by a single heavy-chain complementarity-determining region 3 loop, with minor contacts from heavy-chain complementarity-determining region 1, and is sufficient to achieve nanomolar binding with a minimal footprint. Thus, binding predominantly with a single loop can allow antibodies to target small, conserved functional sites on otherwise hypervariable antigens.