  We classify the translators to the mean curvature flow in the
three-dimensional solvable group $Sol_3$ that are invariant under the action of
a one-parameter group of isometries of the ambient space. In particular we show
that $Sol_3$ admits graphical translators defined on a half-plane, in contrast
with a rigidity result of Shahriyari for translators in the Euclidean space.
Moreover we exhibit some non-existence results.
