Marine sediments records suggest large changes in marine productivity during glacial periods, with abrupt variations especially during the Heinrich events. Here, we study the response of marine biogeochemistry to such an event by using a biogeochemical model of the global ocean (PISCES) coupled to an ocean-atmosphere general circulation model (IPSL-CM4). We conduct a 400-yr-long transient simulation under glacial climate conditions with a freshwater forcing of 0.1 Sv applied to the North Atlantic to mimic a Heinrich event, alongside a glacial control simulation. To evaluate our numerical results, we have compiled the available marine productivity records covering Heinrich events. We find that simulated primary productivity and organic carbon export decrease globally (by 16% for both) during a Heinrich event, albeit with large regional variations. In our experiments, the North Atlantic displays a significant decrease, whereas the Southern Ocean shows an increase, in agreement with paleo-productivity reconstructions. In the Equatorial Pacific, the model simulates an increase in organic matter export production but decreased biogenic silica export. This antagonistic behaviour results from changes in relative uptake of carbon and silicic acid by diatoms. Reasonable agreement between model and data for the large-scale response to Heinrich events gives confidence in models used to predict future centennial changes in marine production. In addition, our model allows us to investigate the mechanisms behind the observed changes in the response to Heinrich events.