This, the scientists said, could generate a cascade of impacts that could push up sea levels, alter weather patterns and starve marine life of a vital source of nutrients.
Prof Matt England, of the Climate Change Research Centre at the University of New South Wales and a co-author of the research published in Nature, said the whole deep ocean current was heading for collapse on its current trajectory.
The research looked at what would happen in the deep ocean around Antarctica if the fresher water melting from ice sheets was added to climate modelling.
The slowdown in the deep ocean current relates to the amount of water that sinks to the bottom and then flows north.
Dr Qian Li, formerly of the University of New South Wales and now at the Massachusetts Institute of Technology, was the lead author of the research, coordinated by England.
In a briefing, the authors said the deep ocean current influenced the climate around the world, with the potential to radically shift rainfall.
England said the slowdown of the deep ocean current caused those deep waters to heat up.
But as that deep water becomes isolated, it could then cause the upper ocean around the continent to get hotter, kicking off a feedback loop where more melting causes accelerated slowing of the current, which then causes more heating and more ice sheet melt.
In a briefing, the scientists said the modelling was in line with recent observations of changes to the deep ocean circulation that was suggesting a slowdown may already be taking place.
The ocean depths were refreshed in only a few places on the planet close to major ice sheets in Greenland and Antarctica.
A slowdown in the deep ocean current could also affect the amount of CO2 that the deep oceans could lock away, Rahmstorf said.
