Annual sea-ice edge phytoplankton blooms occur throughout the Arctic during the spring melt period. Our study considers how phytoplankton spring blooms may depend on sea-ice meltwater. We extend the classic Fisher reaction-diffusion equation to consider a time- and space-varying death rate that represents the role of meltwater in the system. Our results indicate that blooms peak at a characteristic distance from the ice edge where (i) meltwater is still concentrated enough to stratify the upper ocean such that the phytoplankton are confined near the surface and (ii) phytoplankton have been exposed to sufficient sunlight to allow for maximum growth. The results are qualitatively similar to satellite data of a large bloom observed in Fram Strait in May 2019. Our findings support the idea that sea-ice meltwater is of central importance for Arctic phytoplankton blooms.