Ultracold mixtures of different atomic species have great promise for realizing novel many-body phenomena. In a binary mixture of fermions with a large mass difference and repulsive interspecies interactions, a disordered Mott-insulator phase can occur. This phase displays an incompressible total density, although the relative density remains compressible. We use strong-coupling and Monte Carlo calculations to show that this phase exists for a broad parameter region for ultracold gases confined in a harmonic trap on a three-dimensional optical lattice, for experimentally accessible values of the trap parameters.