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Aims.We aim to accurately measure the dynamical mass and distance of Cepheids by combining radial velocity measurements with interferometric observations. Cepheid mass measurements are particularly necessary for solving the Cepheid mass discrepancy, while independent distance determinations provide a crucial test of the period–luminosity relation andGaiaparallaxes. Methods.We used the multi-telescope interferometric combiner, the Michigan InfraRed Combiner (MIRC) of the Center for High Angular Resolution Astronomy (CHARA) Array, to detect and measure the astrometric positions of the high-contrast companion orbiting the Galactic Cepheid SU Cygni. We also present new radial velocity measurements from ultraviolet spectra taken with theHubbleSpace Telescope. The combination of interferometric astrometry with optical and ultraviolet spectroscopy provided the full orbital elements of the system, in addition to component masses and the distance to the Cepheid system. Results.We measured the mass of the Cepheid,M_A = 4.859 ± 0.058 M_⊙, and its two companions,M_Ba = 3.595 ± 0.033 M_⊙andM_Bb = 1.546 ± 0.009 M_⊙. This is the most accurate existing measurement of the mass of a Galactic Cepheid (1.2%). Comparing with stellar evolution models, we show that the mass predicted by the tracks is higher than the measured mass of the Cepheid, which is similar to the conclusions of our previous work. We also measured the distance to the system to be 926.3 ± 5.0 pc, obtaining an unprecedented parallax precision of 6 μas (0.5%), which is the most precise and accurate distance for a Cepheid. This precision is similar to what is expected byGaiafor its last data release (DR5 in ∼2030) for single stars fainter thanG = 13, but is not guaranteed for stars as bright as SU Cyg. Conclusions.We demonstrate that evolutionary models remain incapable of accurately reproducing the measured mass of Cepheids, often predicting higher masses for the expected metallicity, even when factors such as rotation or convective core overshooting are taken into account. Our precise distance measurement allowed us to compare predictions from some period–luminosity relations. We find a disagreement of 0.2–0.5 mag with relations calibrated from photometry, while relations calibrated from a direct distance measurement are in better agreement.