By using the femtosecond laser induced microexplosion method, high-quality two-dimensional eightfold photonic quasicrystals have been fabricated in a solid transparent polymer material. Multiorder band gaps have been observed in a 25-layer structure with a suppression rate of up to 72% for the fundamental gap. Polarization measurements show that the photonic quasicrystal has a strong anisotropic effect, showing that the transverse electric is the favorite polarization. Fabry-Pérot cavities have been fabricated by removing the central layer of channels. Based on the cavity mode position, the order of the mode and the effective cavity size have been determined.