Let A be a (m(1) + m(2)) x (m(1) + m(2)) blocked Wishart random matrix with diagonal blocks of orders m(1) x m(1) and m(2) x m(2). The goal of the paper is to find the exact marginal distribution of the two diagonal blocks of A. We find an expression for this marginal density involving the matrix-variate generalized hypergeometric function. We became interested in this problem because of an application in spatial interpolation of random fields of positive definite matrices, where this result will be used for parameter estimation, using composite likelihood methods.