It is well-known that the Selberg integral is equivalent to the Morris constant term identity. In 2009 Warnaar obtained the Selberg integral for the Lie algebra $A_n$. In this paper, from the point view of constant term identities, we obtain a $q$-Morris constant term identity of type $A_n$ and its several symmetric function generalizations. The type $A_n$ $q$-Morris identity looks as if a constant term version of Warnaar's $A_n$ Selberg integral to some extend.