Terahertz (THz) metamaterial absorbers have realized a prodigious reputation due to the limitation of natural absorbing materials in this range. Getting wideband absorption characteristics is challenging and arduous, especially in the THz band. Self-similar repeated fractal elements offer a promising solution to attain broadband absorption response due to their inherent multiple resonance characteristics. Therefore, by captivating the advantage of fractal geometry, we proposed a dual and wideband meta-absorber operating in the THz regime. The metamaterial absorber design comprises the assembly of self-similar square-shaped blocks arranged in a specific pattern to construct the fractal geometry. The proposed THz absorber demonstrates 90% absorption under normal incident waves for two operating bands from 9.5-10.55 THz and 12.3-13.35 THz. The suggested metamaterial absorber also shows good and stable absorption responses under different oblique incidence angles for transverse electric (TE) and transverse magnetic (TM) wave polarization. Moreover, this absorber manifests over 85% absorptivity in its entire operating range (9-14 THz) under the incidence angle of 60° and 70° for TM mode. Furthermore, it gives a polarization-insensitive behavior under the effect of different polarization angles. This kind of wideband absorber catches fascinating applications in THz detection, imaging, cloaking, and optoelectronic devices.