Can local fluctuations of a ``Quintessence'' scalar field play a dynamical role in the gravitational clustering and cosmic structure formation process? We address this question in the general framework of scalar-tensor theories of gravity. Non-linear energy density perturbations, both in the scalar field and matter component, and linear metric perturbations are accounted for in the perturbed Einstein's equations. We derive the Newtonian limit of the relevant equations for clustering in scalar-tensor cosmologies. We then specialize to non-linear perturbations of the ``Extended Quintessence'' model of Dark Energy; in such a model, a non-minimally coupled scalar field is thought to be responsible for driving the present accelerated phase of the Universe expansion. The interplay between Dark Energy and Dark Matter is displayed in the equations governing the growth of structure in the Universe.

References added; typos corrected; accepted for publication on Phys. Rev. D