Adaptation to future sea-level rise is based on projections of continuously improving climate models. These projections are accompanied by inherent uncertainties, including those due to internal climate variability (ICV). The ICV arises from complex and unpredictable interactions within and between climate-system components, rendering its impact irreducible. Although neglecting this uncertainty can lead to an underestimation of future sea-level rise, its estimation and impacts have not been fully explored. Combining the Community Earth System Model version 1 Large Ensemble experiments with power-law statistics, we show that, by 2100, if the ICV uncertainty reaches its upper limit, new sea-level-rise hotspots would appear in Southeast Asian megacities (Chennai, Kolkata, Yangon, Bangkok, Ho Chi Minh City and Manila), in western tropical Pacific Islands and the Western Indian Ocean. The better the ICV uncertainty is taken into account and correctly estimated, the more effective adaptation strategies can be elaborated with confidence and actions to follow.