  We prove an analogue of the Brauer-Siegel theorem for Fermat surfaces over a
finite field. Namely, letting $F_d$ be the Fermat surface of degree $d$ over
$\mathbb{F}_q$ and $p_g(F_d)$ be its geometric genus, we consider the product
of the order of the Brauer group $\mathrm{Br}(F_d)$ of $F_d$ times the absolute
value of a Gram determinant of the N\'eron-Severi group of $F_d$ with respect
to the intersection form (the regulator $\mathrm{Reg}(F_d)$ of $F_d$). We show
that this product grows like $q^{p_g(F_d)}$ when $d$ tends to infinity: $$
\log\left( |\mathrm{Br}(F_d)|\cdot \mathrm{Reg}(F_d)\right) \sim \log
q^{p_g(F_d)}.$$
