  We determine the minimal number of separating invariants for the invariant
ring of a matrix group $G < \mathrm{GL}_n(\mathbb{F}_q)$ over the finite field
$\mathbb{F}_q$. We show that this minimal number can be obtained with
invariants of degree at most $|G|n(q-1)$. In the non-modular case this
construction can be improved to give invariants of degree at most $n(q-1)$. As
examples we study separating invariants over the field $\mathbb{F}_2$ for two
important representations of the symmetric group
