Primary production, the basic component of the food web and a sink for dissolved inorganic carbon, is a major unknown in Arctic seas, particularly ice algal production, for which detailed and comprehensive studies are often limited in space and time. We present here a simple ice alga model and its coupling with a regional 3D ice–ocean model of the Hudson Bay system (HBS), including Hudson Strait and Foxe Basin, as a first attempt to estimate ice algal production and its potential contribution to the pelagic ecosystem on a regional scale. The ice algal growth rate is forced by sub-ice light and nutrient availability, whereas grazing and ice melt control biomass loss from the underside of the ice. The simulation shows the primary role of sea-ice dynamics on the distribution and production of ice algae with a high spatio-temporal variability in response to the great variability of ice conditions in different parts of the HBS. In addition to favourable light and nutrient conditions, there must be a sufficient time lag between the onset of sufficient light and ice melt to ensure significant ice algal production. This suggests that, in the context of enhanced warming in Arctic and sub-Arctic regions, earlier melt could be more damaging for ice algal production than later freezing. The model also includes a particulate organic matter (POM) variable, fed by ice melting losses to the water column, and shows a large redistribution of the POM produced by the ice ecosystem on a regional scale.