An acoustic panel is provided that includes a perforated first skin, a second skin and a core. The core includes a first wall, a second wall and a stiffener. The core forms a plurality of cavities that extend vertically between the perforated first skin and the second skin and that extend laterally between the first wall and the second wall. The plurality of cavities include a first cavity. The stiffener projects partially into the first cavity and is connect to the first wall and the second wall.