  We study the effect of magnetic field $B$ on the critical temperature $T_{c}$
of the confinement-deconfinement phase transition in hard-wall AdS/QCD, and
holographic duals of flavored and unflavored $\mathcal{N}=4$ super-Yang Mills
theories on $\mathbb{R}^3\times \rm S^1$. For all of the holographic models, we
find that $T_{c}(B)$ decreases with increasing magnetic field $B\ll T^2$,
consistent with the inverse magnetic catalysis recently observed in lattice QCD
for $B\lesssim 1~GeV^2$. We also predict that, for large magnetic field $B\gg
T^2$, the critical temperature $T_{c}(B)$, eventually, starts to increase with
increasing magnetic field $B\gg T^2$ and asymptotes to a constant value.
