  We investigate the interaction caused by quantum gravitational vacuum
fluctuations between a gravitationally polarizable object and a gravitational
boundary, and find a position-dependent energy shift of the object, which
induces a force in close analogy to the Casimir-Polder force in the
electromagnetic case. For a Dirichlet boundary, the explicit form of the
quantum gravitational potential for the polarizable object in its ground-state
is worked out and is found to behave like $z^{-5}$ in the near regime, and
$z^{-6}$ in the far regime, where $z$ is the distance to the boundary. Taking a
Bose-Einstein condensate as a gravitationally polarizable object, we find that
the relative correction to the radius caused by fluctuating quantum
gravitational waves in vacuum is of order $10^{-21}$. Although far too small to
observe in comparison with its electromagnetic counterpart, it is nevertheless
of the order of the gravitational strain caused by a recently detected black
hole merger on the arms of the LIGO.
