Effect of the post-growth annealing on the morphology of a Ge mesa selectively grown on Si was studied from the viewpoint of near-infrared photodiode applications. By ultrahigh-vacuum chemical vapor deposition, Ge mesas were selectively grown at 600 on Si (001) substrates partially covered with SiO2 masks. The as-grown Ge mesas showed trapezoidal cross-sections having a top (001) surface and {311} sidewall facets, as similar to previous reports. However, after the subsequent post-growth annealing at ~800 in the ultrahigh-vacuum chamber, the mesas were deformed into rounded shapes having a depression at the center and mounds near the edges. Such a deformation cannot be observed for the samples annealed once after cooled and exposed to the air. The residual hydrogen atoms on the Ge surface from the germane (GeH4) decomposition is regarded as a trigger to the observed morphological instability, while the final mesa shape is determined in order to minimize a sum of the surface and/or strain energies.