The generalized connectivity of a graph, which was introduced by Chartrand et al. in 1984, is a generalization of the concept of vertex connectivity. Let S be a nonempty set of vertices of G, a collection {T₁,T₂,…,T_r} of trees in G is said to be internally disjoint trees connecting S if E(T_i)∩ E(T_j)=∅ and V(T_i)∩V(T_j)=S for any pair of distinct integers i,j, where 1≤i,j≤r. For an integer k with 2≤k≤n, the k-connectivity κ_k(G) of G is the greatest positive integer r for which G contains at least r internally disjoint trees connecting S for any set S of k vertices of G. Obviously, κ₂(G)=κ(G) is the connectivity of G. Sabidussi's Theorem showed that κ(G ☐ H) ≥κ(G)+κ(H) for any two connected graphs G and H. In this paper, we prove that for any two connected graphs G and H with κ₃(G)≥κ₃(H), if κ(G)>κ₃(G), then κ₃(G ☐ H)≥ κ₃(G)+κ₃(H); if κ(G)=κ₃(G), then κ₃(G ☐ H)≥κ₃(G)+κ₃(H)-1. Our result could be seen as an extension of Sabidussi's Theorem. Moreover, all the bounds are sharp.