  We consider the following nonlinear Schr\"{o}dinger equation with a Hartree
nonlinearity: \[ i\frac{\partial u}{\partial t}+\Delta
u+|u|^{\frac{4}{N}}u\pm\left(\frac{1}{|x|^{2\sigma}}\star|u|^2\right)u=0 \] in
$\mathbb{R}^N$. We are interested in the existence and behaviour of minimal
mass blow-up solutions. Previous studies have shown the existence of minimal
mass blow-up solutions with an inverse power potential and investigated the
behaviour of the solution. In this paper, we investigate Hartree nonlinearity,
which is a nonlinear term similar to the inverse power-type potential in terms
of scaling.
