  A key incentive of quantum gravity is the removal of spacetime singularities
plaguing the classical theory. We compute the non-perturbative
momentum-dependence of a specific structure function within the gravitational
asymptotic safety program which encodes the quantum corrections to the graviton
propagator for momenta above the Planck scale. The resulting quantum corrected
Newtonian potential approaches a constant negative value as the distance
between the two point masses goes to zero, thereby removing the classical
singularity. The generic nature of the underlying mechanism suggests that it
will remain operative in the context of black hole and cosmic singularities.
