The current-climate Indian monsoon is known to boost biological productivity in the Arabian Sea. This paradigm has been extensively used to reconstruct past monsoon variability from palaeo-proxies indicative of changes in surface productivity. Here, we test this paradigm by simulating changes in marine primary productivity for eight contrasted climates from the last glacial–interglacial cycle. We show that there is no straightforward correlation between boreal summer productivity of the Arabian Sea and summer monsoon strength across the different simulated climates. Locally, productivity is fuelled by nutrient supply driven by Ekman dynamics. Upward transport of nutrients is modulated by a combination of alongshore wind stress intensity, which drives coastal upwelling, and by a positive wind stress curl to the west of the jet axis resulting in upward Ekman pumping. To the east of the jet axis there is however a strong downward Ekman pumping due to a negative wind stress curl. Consequently, changes in coastal alongshore stress and/or curl depend on both the jet intensity and position. The jet position is constrained by the Indian summer monsoon pattern, which in turn is influenced by the astronomical parameters and the ice sheet cover. The astronomical parameters are indeed shown to impact wind stress intensity in the Arabian Sea through large-scale changes in the meridional gradient of upper-tropospheric temperature. However, both the astronomical parameters and the ice sheets affect the pattern of wind stress curl through the position of the sea level depression barycentre over the monsoon region (20–150° W, 30° S–60° N). The combined changes in monsoon intensity and pattern lead to some higher glacial productivity during the summer season, in agreement with some palaeo-productivity reconstructions.