Tissue engineering (TE) is a field of regenerative medicine that has been experiencing a special boom in recent years. Among various materials used as components of 3D scaffolds, naturally formed chitinous materials seem to be especially attractive because of their abundance, non-toxic and eco-friendly character. In this study, chitinous skeleton isolated from the marine sponge Aplysina fistularis (phylum: Porifera) was used for the first time as a support for the cultivation of murine fibroblasts (Balb/3T3), human dermal fibroblasts (NHDF), human keratinocyte (HaCaT), and human neuronal (SH-SY5Y) cells. Characterization techniques such as ATR FTIR, TGA, and μCT, clearly indicate that an interconnected macro-porous, thermostable, pure α-chitin scaffold was obtained after alkali–acid treatment of air-dried marine sponge. The biocompatibility of the naturally formed chitin scaffolds was confirmed by cell attachment and proliferation determined by various microscopic methods (e.g., SEM, TEM, digital microscopy) and specific staining. Our observations show that fibroblasts and keratinocytes form clusters on scaffolds that resemble a skin structure, including the occurrence of desmosomes in keratinocyte cells. The results obtained here suggest that the chitinous scaffold from the marine sponge A. fistularis is a promising biomaterial for future research about tissues regeneration.