It is exact in the Newtonian limit, i.e., for speeds slow compared to speed of light, away from strong gravitational fields or horizons, and for big enough objects that quantum effects can be ignored. The 1/r^2 comes from solving Poisson's equation $\nabla^2\phi=4\pi G \rho$. If there would be corrections to this law it would come from additional higher derivative terms. Such higher derivatives would not affect the 1/r^2 behavior at large r. So, in the appropriate limit, yes, it is exact.
It is also extremely well confirmed observationally, since it is the only law that gives elliptical, or stable, planetary orbits.