We report the discovery, mass, and radius determination of TOI-1801 b, a temperate mini-Neptune around a young M dwarf. TOI-1801 b was observed in TESS sectors 22 and 49, and the alert that this was a TESS planet candidate with a period of 21.3 days went out in April 2020. However, ground-based follow-up observations, including seeing-limited photometry in and outside transit together with precise radial velocity (RV) measurements with CARMENES and HIRES revealed that the true period of the planet is 10.6 days. These observations also allowed us to retrieve a mass of 5.74 ± 1.46 M_⊕, which together with a radius of 2.08 ± 0.12 R_⊕, means that TOI-1801 b is most probably composed of water and rock, with an upper limit of 2% by mass of H₂ in its atmosphere. The stellar rotation period of 16 days is readily detectable in our RV time series and in the ground-based photometry. We derived a likely age of 600–800 Myr for the parent star TOI-1801, which means that TOI-1801 b is the least massive young mini-Neptune with precise mass and radius determinations. Our results suggest that if TOI-1801 b had a larger atmosphere in the past, it must have been removed by some evolutionary mechanism on timescales shorter than 1 Gyr.