Recent observations suggest that substantial phytoplankton blooms occur under sea ice on Arctic continental shelves during June and July. This is opposed to the traditional view that no significant biomass is produced in sea-ice covered waters. However, no observational estimates are available on the Arctic-wide primary production beneath sea ice. Here, using a fully-coupled Arctic system model, we estimate that 63% / 41% of the total primary production in the central Arctic occurs in waters covered by sea ice that is >=50% / >=85% concentration. The total primary production there is increasing at a rate of 5.2% per decade during 1980-2018. Increased light transmission, due to the removal of sea ice, more extensive melt ponds, and thinner sea ice, is implicated as the main cause of increasing trends in primary production.