We present the discovery and validation of a super-Earth planet orbiting the M dwarf star TOI-1846 (TIC 198385543). The host star ($K_{\rm mag} = 9.6$) is located 47 pc away and has a radius of $R_\star = 0.41 \pm 0.01$$\rm \, R_\odot$, a mass of $M_\star = 0.40 \pm 0.02$$\rm \, M_\odot$ and an effective temperature of $T_{\rm eff} = 3568 \pm 44$ K. Our analyses are based on joint modelling of Transiting Exoplanet Survey Satellite (TESS) photometry and ground-based multicolour photometric data. We also use high-resolution imaging and archival images, as well as statistical validation techniques to support the planetary system nature. We find that TOI-1846 b is a super-Earth sized planet with radius of $R_{p}=1.79 \pm 0.07$$\rm \, R_{\oplus }$ and a predicted mass of $M_p = 4.4^{+1.6}_{-1.0}$$\rm \, M_{\oplus }$ (from the Chen & Kipping relation) on a 3.9 d orbit, with an equilibrium temperature of $T_{\rm eq}~= 589 \pm 20 K$ (assuming a null Bond Albedo) and an incident flux of $S_p = 17.6 \pm 2.0~S_{\oplus }$. Based on the two radial velocity (RV) measurements obtained with the Tillinghast Reflector Echelle Spectrograph and high-resolution imaging, a non-planetary transiting companion is excluded. With a radius of $\approx$1.8 $\rm \, R_{\oplus }$, TOI-1846 b is within the sparsely populated radius range around 2 $\rm \, R_{\oplus }$ known as the radius gap (or radius valley). This discovery can contribute to refining the precise location of the radius valley for small planets orbiting bright M dwarfs, thereby enhancing our understanding of planetary formation and evolution processes.