The Geometrization of Quantum Mechanics proposed in this work is based on the postulate that the quantum probability density can $curve$ the classical spacetime. It is shown that the gravitational field produced by $smearing$ a point-mass $M_o$ at $ r = 0$ throughout all of space (in an spherically symmetric fashion) can be interpreted as the gravitational field generated by a self-gravitating anisotropic fluid droplet of mass density $ 4 \pi M_o r^2 \varphi^* ( r ) \varphi ( r ) $ and which is sourced by the $probability$ $cloud$ (associated with a spinless point-particle of mass $ M_o$) $permeating$ a $3$-spatial domain region $ {\cal D}_3 = \int 4 \pi r^2 dr $ at any time $ t $. Classically one may smear the point mass in any way we wish leading to arbitrary density configurations $ \rho (r ) $. However, Quantum Mechanically this is $not$ the case because the radial mass configuration $ M (r) $ must obey a key third order nonlinear differential equation (nonlinear extension of the Klein-Gordon equation) displayed in this work and which is the static spherically symmetric relativistic analog of the Newton-Schr\"{o}dinger equation. We conclude by extending our proposal to the Lagrange-Finsler and Hamilton-Cartan geometry of (co) tangent spaces and involving the relativistic version of Bohm's Quantum Potential. By further postulating that the quasi-probability Wigner distribution $W(x,p)$ $curves$ phase spaces, and by encompassing the Finsler-like geometry of the cotangent-bundle with phase space quantum mechanics, one can naturally incorporate the $noncommutative$ and non-local Moyal star product (there are also non-associative star products as well). To conclude, Phase Space is the arena where to implement the space-time-matter unification program. It is our belief this is the right platform where the quantization $of$ spacetime and the quantization $in$ spacetime will coalesce.