Given two DFAs D1 and D2 with n1 and n2 states, respectively, it's possible to construct a new DFA D3 with n1n2 states in it whose language is the intersection of the languages of D1 and D2 by using the product construction: have the states of D correspond to pairs of states, one from D1 and one from D2, and where the accepting states correspond to pairs of accepting states from D1 and D2.
That said, this isn't necessarily going to be the minimum-state DFA for the intersection. It's just going to be some DFA for the intersection.