We describe the first determination of thermal properties and size of the M-type asteroid (16) Psyche from interferometric observations obtained with the Mid-Infrared Interferometric Instrument (MIDI) of the Very Large Telescope Interferometer. We used a thermophysical model to interpret our interferometric data. Our analysis shows that Psyche has a low macroscopic surface roughness. Using a convex 3-D shape model obtained by Kaasalainen et al. (2002, Icarus 159, 369-395), we derived a volume-equivalent diameter for (16) Psyche of 247 +- 25 km or 238 +- 24 km, depending on the possible values of surface roughness. Our corresponding thermal inertia estimates are 133 or 114 J.m-2.s-0.5.K-1, with a total uncertainty estimated to 40 J.m-2.s-0.5.K-1. They are among the highest thermal inertia values ever measured for an asteroid of this size. We consider this as a new evidence of a metal-rich surface for the asteroid (16) Psyche.