  We show that the Modified Newtonian Dynamics (MOND) regime can be fully
recovered as the weak-field limit of a particular theory of gravity formulated
in the metric approach. This is possible when Milgrom's acceleration constant
is taken as a fundamental quantity which couples to the theory in a very
consistent manner. As a consequence, the scale invariance of the gravitational
interaction is naturally broken. In this sense, Newtonian gravity is the
weak-field limit of general relativity and MOND is the weak-field limit of that
particular extended theory of gravity. We also prove that a Noether's symmetry
approach to the problem yields a conserved quantity coherent with this
relativistic MONDian extension.
