The soliton microcomb has sparked interest in high-precision distance measurement, owing to its ultrahigh repetition rate and chip-integrated scale. We report absolute distance measurements based on synthetic wavelength interferometry with a soliton microcomb. We stabilized the repetition rate of 48.98 GHz through injection locking, with fluctuations below 0.25 Hz. Distance measurements up to 64 mm were demonstrated, presenting residuals below 2.7 μm compared with a referenced laser interferometer. Long-term distance measurements were made at two fixed positions of approximately 0.2 m and 1.4 m, resulting in a minimum Allan deviation as low as 56.2 nm at an average time of 0.05 s. The dynamic demonstration illustrated that the proposed system could track round-trip motion of 3 mm at speeds up to 100 mm/s. The proposed distance measurement system is, to our knowledge, the first microcomb-based synthetic wavelength interferometer and achieves a ranging precision of tens of nanometers, with potential applications in the fields of satellite formation flying, high-end manufacturing, and micro-nano processing.