Recently, novel physical consequences of the Extended Relativity Theory in $C$-spaces (Clifford spaces) were explored and which provided a very different physical explanation of the phenomenon of ``relativity of locality" than the one described by the Doubly Special Relativity (DSR) framework. An elegant $nonlinear$ momentum-addition law was derived that tackled the ``soccer-ball'' problem in DSR. Generalized photon dispersion relations allowed also for energy-dependent speeds of propagation while still $retaining$ the Lorentz symmetry in ordinary spacetimes, but breaking the $extended$ Lorentz symmetry in $C$-spaces. This does $not$ occur in DSR nor in other approaches, like the presence of quantum spacetime foam. In this work we show why a $minimal$ length (say the Planck scale) follows naturally from the Extended Relativity principle in Clifford Spaces. Our argument relies entirely on the Physics behind the extended notion of Lorentz transformations in $ C$-space, and $does ~not$ invoke quantum gravity arguments, nor quantum group deformations of Lorentz/Poincare algebras, nor other prior arguments displayed in the Physics literature. The Extended Relativity Theory in Clifford $Phase$ Spaces requires also the introduction of a $maximal$ scale which can be identified with the Hubble scale. It is found also that $ C$-space physics favors a choice of signature $ ( -, +, +, .... , + ) $.