Methods for the analysis of cell secretions at the single-cell level only provide semiquantitative endpoint readouts. Here we describe a microwell array for the real-time spatiotemporal monitoring of extracellular secretions from hundreds of single cells in parallel. The microwell array incorporates a gold substrate with arrays of nanometric holes functionalized with receptors for a specific analyte, and is illuminated with light spectrally overlapping with the device's spectrum of extraordinary optical transmission. Spectral shifts in surface plasmon resonance resulting from analyte-receptor bindings around a secreting cell are recorded by a camera as variations in the intensity of the transmitted light while machine-learning-assisted cell tracking eliminates the influence of cell movements. We used the microwell array to characterize the antibody-secretion profiles of hybridoma cells and of a rare subset of antibody-secreting cells sorted from human donor peripheral blood mononuclear cells. High-throughput measurements of spatiotemporal secretory profiles at the single-cell level will aid the study of the physiological mechanisms governing protein secretion.