  In this paper, we study the entanglement properties of a spin-1 model the
exact ground state of which is given by a Matrix Product state. The model
exhibits a critical point transition at a parameter value a=0. The longitudinal
and transverse correlation lengths are known to diverge as a tends to zero. We
use three different entanglement measures S(i) (the one-site von Neumann
entropy), S(i,j) (the two-body entanglement) and G(2,n) (the generalized global
entanglement) to determine the entanglement content of the MP ground state as
the parameter a is varied. The entanglement length, associated with S(i,j), is
found to diverge in the vicinity of the quantum critical point a=0. The first
derivative of the entanglement measure E (=S(i), S(i,j)) w.r.t. the parameter a
also diverges. The first derivative of G(2,n) w.r.t. a does not diverge as a
tends to zero but attains a maximum value at a=0. At the QCP itself all the
three entanglement measures become zero. We further show that multipartite
correlations are involved in the QPT at a=0.
