The changing climate in the Arctic opens new shipping routes. A shift to shorter Arctic transit will, however, incur a climate penalty over the first one and a half centuries. We investigate the net climate effect of diverting a segment of Europe–Asia container traffic from the Suez to an Arctic transit route. We find an initial net warming for the first one-and-a-half centuries, which gradually declines and transitions to net cooling as the effects of CO2 reductions become dominant, resulting in climate mitigation only in the long term. Thus, the possibilities for shifting shipping to the Arctic confront policymakers with the question of how to weigh a century-scale warming with large uncertainties versus a long-term climate benefit from CO2 reductions.