  In this paper, we consider the dynamics of the solution to the mass critical
focusing Hartree equation with inverse-square potential in the energy space
$H^{1}(\mathbb{R}^d)$. The main difficulties are the equation is \emph{not}
space-translation invariant and the nonlinearity is non-local. We first prove
that if the mass of the initial data is less than that of ground states, then
the solution will be global. Although we don't know whether the ground state is
unique, we can verify all the ground states have the same, minimal mass
threshold. Then at the minimal mass threshold, we can construct the finite-time
blow up solution, which is a pseudo-conformal transformation of the ground
state, up to the symmetries of the equation. Finally, we establish an mass
concentration phenomenon of the finite-time blow up solution to the equation.
