  In this paper we analyze the vacuum polarization effects of a massless scalar
field in the background of a global monopole considering a inner structure to
it. Specifically we investigate the effect of its structure on the vacuum
expectation value of the square of the field operator, $<\hat{\Phi}^2(x)>$,
admitting a non-minimal coupling between the field with the geometry: $\xi
{\cal{R}}\hat{\Phi}^2$. Also we calculate the corrections on the vacuum
expectation value of the energy-momentum tensor, $<\hat{T}_{\mu\nu}>$, due to
the inner structure of the monopole. In order to develop these analysis, we
calculate the Euclidean Green function associated with the system for points in
the region outside the core. As we shall see, for specific value of the
coupling parameter $\xi$, the corrections caused by the inner structure of the
monopole can provide relevant contributions on these vacuum polarizations.
