In this paper, spacelike parallel $p_i$-equidistant ruled surfaces in 3-dimensional Minkowski space $R^3_1$,[1] are generalized to $n$-dimensional Minkowski space $R^3_1$. Then some characteristic results related with algebraic invariants of shape operator of the $(m+1)$-dimensional spacelike parallel $p_i$-equidistant ruled surfaces are given in the Minkowski space $R^n_1$.