The results of studies of the luminescence properties of two-dimensional photonic crystals formed on the basis of silicon structures with self-assembled Ge(Si) nanoislands are reported. The possibilities of substantially enhancing the luminescence response of the active medium (Ge(Si) nanoislands) in the wavelength range 1.2–1.6 μm are shown for such structures. The specific features of the luminescence response of a photonic crystal in the vicinity of the Γ point of its Brillouin zone are studied. It is shown that, along with the broadband response characteristic of the radiative modes of photonic crystals, high-Q resonances, for which the Q factor exceeds 103, can also be observed in such structures. The last-mentioned resonances are observed in a certain range of lattice parameters of photonic crystals.