  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 $\pm$ 1.46 $M_\oplus$, which
together with a radius of 2.08 $\pm$ 0.12 $R_\oplus$, means that TOI-1801 b is
most probably composed of water and rock, with an upper limit of 2\% by mass of
H$_{2}$ 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.
