We present high spatial resolution (≲0.3" ~ 40 AU) Submillimeter Array observations of the 865 µm continuum emission from the circumstellar disk around the young star DoAr 25. Despite its bright millimeter emission, this source exhibits only a comparatively small infrared excess and low accretion rate, suggesting that the material and structural properties of the inner disk may be in an advanced state of evolution. A simple model of the physical conditions in the disk is derived from the submillimeter visibilities and the complete spectral energy distribution using a Monte Carlo radiative transfer code. For the standard assumption of a homogeneous grain size distribution at all disk radii, the results indicate a shallow surface density profile, Σ∝r–p with p~0.34, significantly less steep than a steady-state accretion disk (p=1) or the often adopted minimum mass solar nebula (p=1.5). Even though the total mass of material is large (Md~0.10 M☉), the densities inferred in the inner disk for such a model may be too low to facilitate any mode of planet formation. However, alternative models with steeper density gradients (p~1) can explain the observations equally well if substantial grain growth in the planet formation region (r≤40 AU) has occurred. We discuss these data in the context of such models with dust properties that vary with radius and highlight their implications for understanding disk evolution and the early stages of planet formation.