Let $G$ be a graph of order $n$ and let $k\in \{1,2,\ldots,n-1\}$. The $k$-token graph of $G$ is the graph, whose vertices are all the $k$-subsets of vertices of $G$, where two such $k$-sets are adjacent whenever their symmetric difference is an edge of $G$. In this paper, we determine the automorphism group of the $k$-token graph of the complete bipartite graph $K_{m,n}$.