While covalent drug discovery is reemerging as an important route to small molecule therapeutic leads, strategies for the discovery and engineering of protein-based irreversible binding agents remain limited. Here, we describe the use of yeast display, a high-throughput protein discovery platform, in combination with noncanonical amino acids (ncAAs) to identify irreversible variants of single-domain antibodies (sdAbs), also called VHHs and nanobodies, targeting botulinum neurotoxin light chain A (LC/A). Starting from a series of previously described, structurally characterized sdAbs, we evaluated the properties of antibodies substituted with reactive ncAAs capable of forming covalent bonds with nearby groups after UV irradiation (when using 4-azido-L-phenylalanine) or spontaneously (when using O-(2-bromoethyl)-L-tyrosine). Systematic evaluations in yeast display format of more than 40 ncAA-substituted variants revealed numerous clones that retain binding function while gaining either UV-mediated or spontaneous crosslinking capabilities. Solution-based analyses indicate that ncAA-substituted clones exhibit site-dependent target specificity and crosslinking capabilities uniquely conferred by ncAAs. Interestingly, not all ncAA substitution sites resulted in crosslinking events, and our data showed no apparent correlation between detected crosslinking levels and distances between sdAbs and LC/A residues. This underscores the utility of high-throughput platforms both to identify crosslinkable antibodies and to inform future rational and computational designs of such antibodies. Our findings highlight the power of yeast display in combination with genetic code expansion in the discovery of binding agents that covalently engage their targets. This platform streamlines the discovery and characterization of antibodies with therapeutically relevant properties that cannot be accessed in the conventional genetic code.