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The rapid loss of sea ice in the Arctic is one of the most striking manifestations of climate change. As sea ice melts, more open water is exposed to solar radiation, absorbing heat and generating a sea-ice–albedo feedback that reinforces Arctic warming. Recent studies stress the significance of this feedback mechanism and suggest that ice-free summer conditions in the Arctic Ocean may occur faster than previously expected, even under low-emissions pathways. Here we use an integrated assessment model to explore the implications of a potentially rapid sea-ice-loss process. We consider a scenario leading to a full month free of sea ice in September 2050, followed by three potential trajectories afterward: partial recovery, stabilization, and continued loss of sea ice. We analyze how these scenarios affect the efforts to keep global temperature increase below 2°C. Our results show that sea-ice melting in the Arctic requires more stringent mitigation efforts globally. We find that global CO2 emissions would need to reach zero levels 5–15 years earlier and that the carbon budget would need to be reduced by 20%–51% to offset this additional source of warming. The extra mitigation effort would imply an 18%–59% higher mitigation cost to society. Our results also show that to achieve the 1.5°C target in the presence of ice-free summers negative emissions would be needed. This study highlights the need for a better understanding of how the rapid changes observed in the Arctic may impact our society.