Direct products and the contravariant hom-functor

We prove in ZFC that if $G$ is a (right) $R$-module such that the groups ${\text{Hom}}_R({\prod }_{i\in I}{G}_i,G)$ and ${\prod }_{i\in I}{\text{Hom}}_R(G_i,G)$ are naturally isomorphic for all families of $R$-modules $(G_i{)}_{i\in I}$ then G=0. The result is valid even we restrict to families such that $G_i\cong G$ for all $i\in I$.