Prominent K-shell emission lines of neutral iron (hereafter Fe I-K lines) and hard-continuum X-rays from molecular clouds (MCs) in the Sagittarius B (Sgr B) region were found in two separate Suzaku observations in 2005 and 2009. The X-ray flux of the Fe I-K lines decreased in correlation with the hard-continuum flux by a factor of 0.4-0.5 in four years, which is almost equal to the light traveling across the MCs. The rapid and correlated time variability, the equivalent width of the Fe I-K lines, and the K edge absorption depth of Fe I are consistently explained by 'X-ray echoes' due to the fluorescent and Thomson scattering of an X-ray flare from an external source. The required flux of the X-ray flare depends on the distance to the MCs and its time duration. Even for a case with a minimum distance, the flux is larger than those of the brightest Galactic X-ray sources. Based on these facts, we conclude that the supermassive black hole Sgr A* exhibited a large flare a few hundred years ago with a luminosity of more than 4 X 1039 erg s--1. The 'X-ray echo' from Sgr B, located a few hundred light-years from Sgr A*, has now reached the Earth.