By means of near-simultaneous multi-wavelength VLBA measurements, we determine for the first time the intrinsic size of Sgr A* to be 3.6 AU by <1 AU with the major axis oriented essentially north-south. Contrary to previous expectation that the intrinsic structure of Sgr A* is observable only at wavelength shorter than 1 mm, we can discern the intrinsic source size at 7~mm because (1) the scattering size along the minor axis is half that along the major axis, and (2) the near simultaneous multi-wavelength mapping of Sgr A* makes it possible to extrapolate precisely the minor axis scattering angle at 7~mm. The intrinsic size and shape place direct constraints on the various theoretical models for Sgr A*.