We apply our novel Markov Chain Monte Carlo (MCMC)–based algorithm for asteroid mass estimation to asteroid (16) Psyche, the target of NASA's eponymous Psyche mission, based on close encounters with 10 different asteroids, and obtain a mass of (1.117 ± 0.039) × 10⁻¹¹ M_⊙. We ensure that our method works as expected by applying it to asteroids (1) Ceres and (4) Vesta, and find that the results are in agreement with the very accurate mass estimates for these bodies obtained by the Dawn mission. We then combine our mass estimate for Psyche with the most recent volume estimate to compute the corresponding bulk density as (3.88 ± 0.25) g cm⁻³. The estimated bulk density rules out the possibility of Psyche being an exposed, solid iron core of a protoplanet, but is fully consistent with the recent hypothesis that ferrovolcanism would have occurred on Psyche.