We present the discovery of an exceptional dimming event in a cool supergiant star in the Local Volume spiral M51. The star, dubbed M51-DS1, was found as part of a Hubble Space Telescope (HST) search for failed supernovae (SNe). The supergiant, which is plausibly associated with a very young (<~6Myr) stellar population, showed clear variability (amplitude {Delta}F814W~0.7mag) in numerous HST images obtained between 1995 and 2016, before suddenly dimming by >2mag in F814W sometime between late 2017 and mid-2019. In follow-up data from 2021, the star rebrightened, ruling out a failed supernova. Prior to its near-disappearance, the star was luminous and red (M_F814W_<~-7.6mag, F606W-F814W=1.9-2.2mag). Modeling of the pre-dimming spectral energy distribution of the star favors a highly reddened, very luminous (log[L/L_{sun}_]=5.4-5.7) star with Teff~3700-4700K, indicative of a cool yellow or post-red supergiant (RSG) with an initial mass of ~26-40M_{sun}_. However, the local interstellar extinction and circumstellar extinction are uncertain, and could be lower: the near-IR colors are consistent with an RSG, which would be cooler (Teff<~3700K) and slightly less luminous (log[L/L_{sun}_]=5.2-5.3), giving an inferred initial mass of ~19-22M_{sun}_. In either case, the dimming may be explained by a rare episode of enhanced mass loss that temporarily obscures the star, potentially a more extreme counterpart to the 2019-2020 "Great Dimming" of Betelgeuse. Given the emerging evidence that massive evolved stars commonly exhibit variability that can mimic a disappearing star, our work highlights a substantial challenge in identifying true failed SNe.