A set of vertices S mixed-resolves a graph G if every vertices or edges is uniquely determined by its vector of distances to the vertices in S. The mixed metric dimension of G is the minimum cardinality of a mixed resolving set of G. This paper studies some upper bounds for the mixed metric dimensions of the Cartesian product for any given graph G and H and the exact value of the mixed metric dimension of the Cartesian product for a particular graph G and H.