For a connected graph \( G \), the Wiener index \( W \) and the Harary index \( H \) are defined as \( W=\sum_{u,v}d(u,v) \) and \( H=\sum_{u,v}1/d(u,v) \), respectively. In this paper, the product \( W\cdot H \) is first extended to hypergraphs. We determine the unique \( k \)-uniform hypergraphs with maximum, minimum and second minimum \( W\cdot H \)-value, respectively.