We report the discovery of one super-Earth- (TOI-1749b) and two sub-Neptune-sized planets (TOI-1749c and TOI-1749d) transiting an early M dwarf at a distance of 100 pc, which were first identified as planetary candidates using data from the TESS photometric survey. We have followed up this system from the ground by means of multiband transit photometry, adaptive optics imaging, and low-resolution spectroscopy, from which we have validated the planetary nature of the candidates. We find that TOI-1749b, c, and d have orbital periods of 2.39, 4.49, and 9.05 days, and radii of 1.4, 2.1, and 2.5 R⊕, respectively. We also place 95% confidence upper limits on the masses of 57, 14, and 15 M⊕ for TOI-1749b, c, and d, respectively, from transit timing variations. The periods, sizes, and tentative masses of these planets are in line with a scenario in which all three planets initially had a hydrogen envelope on top of a rocky core, and only the envelope of the innermost planet has been stripped away by photoevaporation and/or core-powered mass-loss mechanisms. These planets are similar to other planetary trios found around M dwarfs, such as TOI-175b,c,d and TOI-270b,c,d, in the sense that the outer pair has a period ratio within 1% of 2. Such a characteristic orbital configuration, in which an additional planet is located interior to a near 2:1 period-ratio pair, is relatively rare around FGK dwarfs.