The Event Horizon Telescope has recently provided the first image of the dark shadow around the supermassive black hole M87*. The observation of a highly circular shadow provides strong limits on deviations of M87*'s quadrupole moment from the Kerr value. We show that the absence of such a deviation can be used to constrain the physics of extra dimensions of spacetime. Focusing on the Randall-Sundrum AdS(5) brane-world scenario, we show that the observation of M87*'s dark shadow sets the limit l less than or similar to 170 AU, where l is the AdS(5) curvature radius. This limit is among the first quantitative constraints on exotic physics obtained from the extraordinary first ever image of the dark shadow of a black hole.