We present radio observations of the tidal disruption event candidate (TDE) XMMSL1 J0740−85 spanning 592 to 875 days post X-ray discovery. We detect radio emission that fades from an initial peak flux density at 1.6 GHz of 1.19 0.06 mJy to 0.65 0.06 mJy, suggesting an association with the TDE. This makes XMMSL1 J0740−85 at d = 75 Mpc the nearest TDE with detected radio emission to date and only the fifth TDE with radio emission overall. The observed radio luminosity rules out a powerful relativistic jet like that seen in the relativistic TDE Swift J1644+57. Instead, we infer from an equipartition analysis that the radio emission most likely arises from a non-relativistic outflow similar to that seen in the nearby TDE ASASSN-14li, with a velocity of about 104 km s−1 and a kinetic energy of about 1048 erg, expanding into a medium with a density of about 102 cm−3. Alternatively, the radio emission could arise from a weak initially relativistic but decelerated jet with an energy of erg, or (for an extreme disruption geometry) from the unbound debris. The radio data for XMMSL1 J0740−85 continues to support the previous suggestion of a bimodal distribution of common non-relativistic isotropic outflows and rare relativistic jets in TDEs (in analogy with the relation between Type Ib/c supernovae and long-duration gamma-ray bursts). The radio data also provide a new measurement of the circumnuclear density on a sub-parsec scale around an extragalactic supermassive black hole.