Given a connected graph $G$, the equidistant dimension of $G$ represents the cardinality of the smallest set of vertices $S$ of $G$ such that for any two vertices $x,y\notin S$ there is at least one vertex in $S$ equidistant to both $x,y$ in terms of distances. In this article, we compute the equidistant dimension of some Cartesian product graphs including two-dimensional Hamming graphs, some hypercubes, prisms of cycle, and squared grid graphs.