We report the confirmation and mass determination of a mini-Neptune transiting the M3.5 V star TOI-4438 (G 182-34) every 7.44 days. A transit signal was detected with NASA's TESS space mission in the sectors 40, 52, and 53. In order to validate the planet TOI-4438 b and to determine the system properties, we combined TESS data with high-precision radial velocity measurements from the CARMENES spectrograph, spanning almost one year, and ground-based transit photometry. We found that TOI-4438 b has a radius of Rb = 2.52 ± 0.13 R⊕ (5% precision), which together with a mass of Mb = 5.4 ± 1.1 M⊕ (20% precision), results in a bulk density of ρb = 1.85−0.44+0.51 g cm−3 (~28% precision), aligning the discovery with a volatile-rich planet. Our interior structure retrieval with a pure water envelope yields aminimum water mass fraction of 46% (1σ). TOI-4438 b is a volatile-rich mini-Neptune with likely H/He mixed with molecules, such as water, CO2, and CH4. The primary star has a J-band magnitude of 9.7, and the planet has a high transmission spectroscopy metric (TSM) of 136 ± 13. Taking into account the relatively warm equilibrium temperature of Teq = 435 ± 15 K, and the low activity level of its host star, TOI-4438 b is one of the most promising mini-Neptunes around an M dwarf for transmission spectroscopy studies.