We employ numerical simulations and simple analytical estimates to argue that dark matter substructures orbiting in the inner regions of the Galaxy can be efficiently destroyed by disk shocking, a dynamical process known to affect globular star clusters. We carry out a set of fiducial high-resolution collisionless simulations in which we adiabatically grow a disk, allowing us to examine the impact of the disk on the substructure abundance. We also track the orbits of dark matter satellites in the high-resolution Aquarius simulations and analytically estimate the cumulative halo and disk shocking effect. Our calculations indicate that the presence of a disk with only 10% of the total Milky Way mass can significantly alter the mass function of substructures in the inner parts of halos. This has important implications especially for the relatively small number of satellites seen within ~30 kpc of the Milky Way center, where disk shocking is expected to reduce the substructure abundance by a factor of ~2 at 10^9 M$_{⊙}$ and ~3 at 10^7 M$_{⊙}$. The most massive subhalos with 10^10 M$_{⊙}$ survive even in the presence of the disk. This suggests that there is no inner missing satellite problem, and calls into question whether these substructures can produce transient features in disks, like multi-armed spiral patterns. Also, the depletion of dark matter substructures through shocking on the baryonic structures of the disk and central bulge may aggravate the problem to fully account for the observed flux anomalies in gravitational lens systems, and significantly reduces the dark matter annihilation signal expected from nearby substructures in the inner halo. ; Comment: 10 pages, 9 figures, minor corrections, accepted by ApJ