The velocity field of UCD3 shows the signature of weak rotation, comparable to that found in massive globular clusters. Its velocity dispersion profile is fully consistent with an isotropic velocity distribution and the assumption that mass follows the light distribution obtained from Hubble Space Telescope imaging. In particular, there is no evidence for the presence of an extended dark matter halo contributing a significant (greater than or similar to 33 per cent within R < 200 pc) mass fraction, nor for a central black hole more massive than similar to 5 per cent of the UCD's mass. While this result does not exclude a galaxian origin for UCD3, we conclude that its internal kinematics are fully consistent with it being a massive star cluster.