- A process of single diffractive dissociation off nuclei is considered on a basis of solutions to the nonlinear evolution equation. The relevant saturation scales Q s AD (x, x 0) are determined and their dependences on Bjorken x, atomic number A, and minimal rapidity gap Y 0≡ ln 1/x 0 are investigated. The solutions are shown to possess a geometrical scaling in a broad kinematic region for x well below x 0. The ratio σ diff/σ tot is computed for several nuclei. We predict that at x≃ 10− 4 this ratio is of the order 25% which is much larger compared to the one of proton. This result indicates a possibility to observe a very strong nuclear shadowing.