  In this paper, the boundedness properties of vector-valued intrinsic square
functions and their vector-valued commutators with $BMO(\mathbb R^n)$ functions
are discussed. We first show the weighted strong type and weak type estimates
of vector-valued intrinsic square functions in the Morrey type spaces. Then we
obtain weighted strong type estimates of vector-valued analogues of commutators
in Morrey type spaces. In the endpoint case, we establish the weighted weak
$L\log L$-type estimates for these vector-valued commutators in the setting of
weighted Lebesgue spaces. Furthermore, we prove weighted endpoint estimates of
these commutator operators in Morrey type spaces. In particular, we can obtain
strong type and endpoint estimates of vector-valued intrinsic square functions
and their commutators in the weighted Morrey spaces and the generalized Morrey
spaces.
