  Let $S$ be a scheme and let $\pi : \mathcal{G} \to S$ be a
$\mathbb{G}_{m,S}$-gerbe corresponding to a torsion class $[\mathcal{G}]$ in
the cohomological Brauer group $\mathrm{Br}'(S)$ of $S$. We show that the
cohomological Brauer group $\mathrm{Br}'(\mathcal{G})$ of $\mathcal{G}$ is
isomorphic to the quotient of $\mathrm{Br}'(S)$ by the subgroup generated by
the class $[\mathcal{G}]$. This is analogous to a theorem proved by Gabber for
Brauer-Severi schemes.
