  We show that any analytic $f(R)$-gravity model, in the metric approach,
presents a weak field limit where the standard Newtonian potential is corrected
by a Yukawa-like term. This general result has never been pointed out but often
derived for some particular theories. This means that only $f(R)=R$ allows to
recover the standard Newton potential while this is not the case for other
relativistic theories of gravity. Some considerations on the physical
consequences of such a general solution are addressed.
