In this paper, we studied the sharp bounds for the $m$-linear $n$-dimensional $p$-adic integral operator with a kernel on central and noncentral $p$-adic Morrey spaces with power weight. As an application, the sharp bounds for $p$-adic Hardy and Hilbert operators on $p$-adic weighted Morrey spaces were obtained. Finally, we also found the sharp bound for the $p$-adic Hausdorff operator on $p$-adic weighted central and noncentral Morrey spaces, which generalizes the previous results.