An ultrasonic MEMS acoustic transducer formed in a body of semiconductor material having first and second surfaces opposite to one another. A first cavity extends in the body and delimits at the bottom a sensitive portion, which extends between the first cavity and the first surface of the body. The sensitive portion houses a second cavity and forms a membrane that extends between the second cavity and the first surface of the body. An elastic supporting structure extends between the sensitive portion and the body and is suspended over the first cavity.