Common genetic variants across individuals modulate the cellular response to pathogens and are implicated in diverse immune pathologies, yet how they dynamically alter the response upon infection is not well understood. Here, we triggered antiviral responses in human fibroblasts from 68 healthy donors, and profiled tens of thousands of cells using single-cell RNA-sequencing. We developed GASPACHO (GAuSsian Processes for Association mapping leveraging Cell HeterOgeneity), a statistical approach designed to identify nonlinear dynamic genetic effects across transcriptional trajectories of cells. This approach identified 1,275 expression quantitative trait loci (local false discovery rate 10%) that manifested during the responses, many of which were colocalized with susceptibility loci identified by genome-wide association studies of infectious and autoimmune diseases, including theOAS1splicing quantitative trait locus in a COVID-19 susceptibility locus. In summary, our analytical approach provides a unique framework for delineation of the genetic variants that shape a wide spectrum of transcriptional responses at single-cell resolution.