  The simple integrable modules with finite dimensional weight spaces are
classified for the quantum affine special linear superalgebra
$\U_q(\hat{\mathfrak{sl}}(M|N))$ at generic $q$. Any such module is shown to be
a highest weight or lowest weight module with respect to one of the two natural
triangular decompositions of the quantum affine superalgebra depending on
whether the level of the module is zero or not. Furthermore, integrable
$\U_q(\hat{\mathfrak{sl}}(M|N))$-modules at nonzero levels exist only if $M$ or
$N$ is $1$.
