  We study the gravitational field of static p-branes in D-dimensional
Minkowski space in the framework of linearized ghost-free (GF) gravity. The
concrete models of GF gravity we consider are parametrized by the non-local
form factors $\exp(-\Box/\mu^2)$ and $\exp(\Box^2/\mu^4)$, where $\mu^{-1}$ is
the scale of non-locality. We show that the singular behavior of the
gravitational field of p-branes in General Relativity is cured by short-range
modifications introduced by the non-localities, and we derive exact expressions
of the regularized gravitational fields, whose geometry can be written as a
warped metric. For large distances compared to the scale of non-locality, $\mu
r\rightarrow\infty$, our solutions approach those found in linearized General
Relativity.
