Some universities do, but it's not a nationally mandated thing as far as I know.
I'm a domestic graduate student at a university that requires TOEFL scores (http://www.ets.org/toefl) and my department is rumored to have a policy of calling international students they are strongly considering in order to double check they can hold an intelligible conversation in English. That said, you can still get students who aren't very strong in "conversational/professional speaking level" English who pass through these requirements.