  We prove an $\mathbb F_p$-Selberg integral formula of type $A_n$, in which
the $\mathbb F_p$-Selberg integral is an element of the finite field $\mathbb
F_p$ with odd prime number $p$ of elements. The formula is motivated by analogy
between multidimensional hypergeometric solutions of the KZ equations and
polynomial solutions of the same equations reduced modulo $p$. For the type
$A_1$ the formula was proved in a previous paper by the authors.
