Primary production is a key marine ecosystem driver in the Bay of Bengal and is important for the societies and economies of the surrounding countries. Although the availability of inorganic nutrients is known to control primary production in this region, the specific nutrient sources that affect primary production in different parts of the bay have not been identified. In this study, we assess the importance of nutrients from different sources in determining chlorophyll-a concentration, an indicator of primary production, in the Bay of Bengal by conducting multiple linear regression of satellite-derived chlorophyll-a concentration, sea surface height anomaly, and sea surface temperature; modelled dust deposition; and in situ river discharge from 1997 to 2016. River-borne nutrients were important up to approximately 200 km from the coast. Deep-ocean nutrients influenced chlorophyll-a concentrations mainly in the south-western and western bay, whereas wind-borne nutrients were more important in the central and eastern bay. Any attempt to understand the impact of nutrients from a certain source should also consider the potential impacts of other nutrient sources. Although climate impacts on chlorophyll-a concentrations through river discharge were observed in our study, future studies should investigate climate-change impacts through atmospheric aerosols and mesoscale eddies.