We report the discovery of TOI-1268b, a transiting Saturn-mass planet from the TESS space mission. With an age of less than 1 Gyr, derived from various age indicators, TOI-1268b is the youngest Saturn-mass planet known to date; it contributes to the small sample of well-characterised young planets. It has an orbital period of P = 8.1577080 ± 0.0000044 days, and transits an early K-dwarf star with a mass of M* = 0.96 ± 0.04 M⊙, a radius of R* = 0.92 ± 0.06 R⊙, an effective temperature of Teff = 5300 ± 100 K, and a metallicity of 0.36 ± 0.06 dex. By combining TESS photometry with high-resolution spectra acquired with the Tull spectrograph at the McDonald Observatory, and the high-resolution spectrographs at the Tautenburg and Ondřejov Observatories, we measured a planetary mass of Mp = 96.4 ± 8.3 M⊕ and a radius of Rp = 9.1 ± 0.6 R⊕. TOI-1268 is an ideal system for studying the role of star-planet tidal interactions for non-inflated Saturn-mass planets. We used system parameters derived in this paper to constrain the planet's tidal quality factor to the range of 104.5-5.3. When compared with the sample of other non-inflated Saturn-mass planets, TOI-1268b is one of the best candidates for transmission spectroscopy studies.