  Many generic arguments support the existence of a minimum spacetime interval
$L_0$. Such a "zero-point" length can be naturally introduced in a locally
Lorentz invariant manner via Synge's world function bi-scalar $\Omega(p,P)$
which measures squared geodesic interval between spacetime events $p$ and $P$.
I show that there exists a \emph{non-local} deformation of spacetime geometry
given by a \emph{disformal} coupling of metric to the bi-scalar $\Omega(p,P)$,
which yields a geodesic interval of $L_0$ in the limit $p \rightarrow P$.
Locality is recovered when $\Omega(p,P) >> L_0^2/2$. I discuss several
conceptual implications of the resultant small-scale structure of spacetime for
QFT propagators as well as spacetime singularities.
