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Moons potentially harbouring a global ocean are tending to become relatively common objects in the Solar System1. The presence of these long-lived global oceans is generally betrayed by surface modification owing to internal dynamics2. Hence, Mimas would be the most unlikely place to look for the presence of a global ocean3. Here, from detailed analysis of Mimas’s orbital motion based on Cassini data, with a particular focus on Mimas’s periapsis drift, we show that its heavily cratered icy shell hides a global ocean, at a depth of 20–30 kilometres. Eccentricity damping implies that the ocean is likely to be less than 25 million years old and still evolving. Our simulations show that the ocean–ice interface reached a depth of less than 30 kilometres only recently (less than 2–3 million years ago), a time span too short for signs of activity at Mimas’s surface to have appeared.