In this Letter, we report the discovery of an ultraluminous fast-evolving transient in rest-frame UV wavelengths, MUSSES2020J, soon after its occurrence by using the Hyper Suprime-Cam (HSC) mounted on the 8.2 m Subaru telescope. The rise time of about 5 days with an extremely high UV peak luminosity shares similarities to a handful of fast blue optical transients whose peak luminosities are comparable with the most luminous supernovae while their timescales are significantly shorter (hereafter "fast blue ultraluminous transient," FBUT). In addition, MUSSES2020J is located near the center of a normal low-mass galaxy at a redshift of 1.063, suggesting a possible connection between the energy source of MUSSES2020J and the central part of the host galaxy. Possible physical mechanisms powering this extreme transient such as a wind-driven tidal disruption event and an interaction between supernova and circumstellar material are qualitatively discussed based on the first multiband early-phase light curve of FBUTs, although whether the scenarios can quantitatively explain the early photometric behavior of MUSSES2020J requires systematical theoretical investigations. Thanks to the ultrahigh luminosity in UV and blue optical wavelengths of these extreme transients, a promising number of FBUTs from the local to the high-z universe can be discovered through deep wide-field optical surveys in the near future.