  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$_{\odot}$ and
  ~3 at 10^7 M$_{\odot}$. The most massive subhalos with 10^10
  M$_{\odot}$ 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.
