Summary: The \(k\)-ary \(n\)-cube, \(Q^k_n\), is one of the most popular interconnection networks. Let \(n\geq 2\) and \(k\geq 3\). It is known that \(Q^k_n\) is a nonbipartite (resp. bipartite) graph when \(k\) is odd (resp. even). In this paper we prove that there exist \(r\) vertex disjoint paths \(\{P_{i}\mid 0\leq i\leq r - 1\}\) between any two distinct vertices \(u\) and \(v\) of \(Q^k_n\) when \(k\) is odd, and there exist \(r\) vertex disjoint paths \(\{R_{i}\mid 0\leq i\leq r - 1\}\) between any pair of vertices \(w\) and \(b\) from different partite sets of \(Q^k_n\) when \(k\) is even, such that \(\bigcup^{r-1}_{i=0}P_i\) or \(\bigcup^{r-1}_{i=0}R_i\) covers all vertices of \(Q^k_n\) for \(1\leq r\leq 2n\). In other words, we construct the one-to-one \(r\)-disjoint path cover of \(Q^k_n\) for any \(r\) with \(1\leq r\leq 2n\). The result is optimal since any vertex in \(Q^k_n\) has exactly \(2n\) neighbors.