As a key persistent component of the atmospheric dynamics, the North Atlantic blocking activity has been linked to extreme climatic phenomena in the European sector. It has also been linked to Atlantic multidecadal ocean variability, but its potential links to rapid oceanic changes have not been investigated. Using a global ocean-sea ice model forced with atmospheric reanalysis data, here it is shown that the 1962-1966 period of enhanced blocking activity over Greenland resulted in anomalous sea ice accumulation in the Arctic and ended with a sea ice flush from the Arctic into the North Atlantic Ocean through Fram Strait. This event induced a significant decrease of Labrador Sea water surface salinity and an abrupt weakening of the Atlantic Meridional Overturning Circulation (AMOC) during the 1970s. These results have implications for the prediction of rapid AMOC changes and indicate that an important part of the atmosphere-ocean dynamics at mid- and high latitudes requires a proper representation of the Fram Strait sea ice transport and of the synoptic scale variability such as atmospheric blocking, which is a challenge for current coupled climate models.