  We construct exact pp-wave solutions of ghost-free infinite derivative
gravity and demonstrate that the sourceless theory does not bring any pp-wave
solutions save for that of Einstein's gravity. These waves described in the
Kerr-Schild form also solve the linearized field equations of the theory. We
also find an exact gravitational shock wave with non-singular curvature
invariants and with a finite limit in the ultraviolet regime of non-locality
which is in contrast to the divergent limit in Einstein's theory.
