  Finsler geometry is a well known generalization of Riemannian geometry which
allows to account for a possibly non trivial structure of the space of
configurations of relativistic particles. We here establish a link between
Finsler geometry and the sort of models with curved momentum space and
DSR-relativistic symmetries which have been recently of interest in the
quantum-gravity literature. We use as case study the much-studied scenario
which is inspired by the $\kappa$-Poincar\'e quantum group, and show that the
relevant deformation of relativistic symmetries can be implemented within a
Finsler geometry.
