We investigate the properties of the photonic band structure (PBS) of Fibonacci superlattices (FS) containing metamaterial absorptive layers. We study the properties of the PBS by the transfer matrix method (TMM). The energetic transmission coefficient for polarized light falling oblique on finite and binary FS placed in free space is calculated. The numerical results concerning transmission bands and energetic absorption coefficient are presented. The existence of fractal properties of PBS, and so called zero- gaps are confirmed in moustaches-like transmission spectra. The absorption effects are also discussed.