We show that the prompt and afterglow X-ray emission of GRB 060218, as well as its early (t 1 day) optical-UV emission, can be explained by a model in which a radiation-mediated shock propagates outward from a compact progenitor star into a dense wind. The prompt thermal X-ray emission is produced in this model when the mildly relativistic shock, β ≈ 0.85, carrying a few times 10⁴⁹ erg, reaches the wind (Thomson) photosphere, where the postshock thermal radiation is released and the shock becomes collisionless. Adopting this interpretation of the thermal X-ray emission, we predict a subsequent X-ray afterglow, due to synchrotron emission and inverse Compton scattering of supernova UV photons by electrons accelerated in the collisionless shock. Early optical-UV emission is also predicted, due to the cooling of the outer δM ~ 10^-3 M envelope of the star, which was heated to high temperature during the shock passage. The observed X-ray afterglow and the early optical-UV emission are both consistent with those expected in this model. Detailed analysis of the early optical-UV emission may provide detailed constraints on the density distribution near the stellar surface.