Apical membrane antigen 1 (AMA1) is essential for invasion of erythrocytes and hepatocytes by Plasmodium parasites and is a leading malarial vaccine candidate. Although conventional antibodies to AMA1 can prevent such invasion, extensive polymorphisms within surface-exposed loops may limit the ability of these AMA1-induced antibodies to protect against all parasite genotypes. Using an AMA1-specific IgNAR single-variable-domain antibody, we performed targeted mutagenesis and selection against AMA1 from three P. falciparum strains. We present cocrystal structures of two antibody-AMA1 complexes which reveal extended IgNAR CDR3 loops penetrating deep into a hydrophobic cleft on the antigen surface and contacting residues conserved across parasite species. Comparison of a series of affinity-enhancing mutations allowed dissection of their relative contributions to binding kinetics and correlation with inhibition of erythrocyte invasion. These findings provide insights into mechanisms of single-domain antibody binding, and may enable design of reagents targeting otherwise cryptic epitopes in pathogen antigens.