Monoclonal antibodies are increasingly used to prevent and treat viral infections and are pivotal in pandemic response efforts. Antibody-secreting cells (ASCs; plasma cells and plasmablasts) are an excellent source of high-affinity antibodies with therapeutic potential. Current methods to study antigen-specific ASCs either have low throughput, require expensive and labor-intensive screening or are technically demanding and therefore not widely accessible. Here we present a straightforward technology for the rapid discovery of monoclonal antibodies from ASCs. Our approach combines microfluidic encapsulation of single cells into an antibody capture hydrogel with antigen bait sorting by conventional flow cytometry. With our technology, we screened millions of mouse and human ASCs and obtained monoclonal antibodies against severe acute respiratory syndrome coronavirus 2 with high affinity (<1 pM) and neutralizing capacity (<100 ng ml-1) in 2 weeks with a high hit rate (>85% of characterized antibodies bound the target). By facilitating access to the underexplored ASC compartment, the approach enables efficient antibody discovery and immunological studies into the generation of protective antibodies.