  We consider a mass critical nonlinear Schr\"{o}dinger equation with a
real-valued potential. In this work, we construct a minimal mass solution that
blows up at finite time, under weaker assumptions on spatial dimensions and
potentials than Banica, Carles, and Duyckaerts (2011). Moreover, we show that
the blow-up solution converges to a blow-up profile. Furthermore, we improve
some parts of the arguments in Rapha\"{e}l and Szeftel (2011) and Le Coz,
Martel, and Rapha\"{e}l (2016).
