Cellulose nanocrystal (CNC)-based hydrogels are considered attractive biomaterials for tissue engineering due to their excellent physicochemical properties. Hydrogels of alginate and gelatin were prepared with or without CNCs and printed using a CELLINK® BIOX 3D bio-printer. The 3D-printed scaffolds were characterized by Fourier transform infrared (FTIR) spectroscopy, Raman spectroscopy, transmission electron microscopy (TEM), and scanning electron microscopy (SEM). Improved mechanical strength was observed in the composite scaffolds compared to the pure polymer scaffolds. Fabricated scaffolds exhibited superior swelling potential; this property is profoundly affected by the CNC content of hydrogels. Biocompatibility of the fabricated scaffolds was monitored in the presence of human bone marrow-derived mesenchymal stem cells (hBMSCs) using the WST-1 assay. Notably, better cell viability was observed in the composite scaffolds than in the control, indicating improved biocompatibility of composites. Cells were healthy and adhered appropriately to the surface of the scaffolds. Mineralization potential of the prepared scaffolds was evaluated by the alizarin red S (ARS) staining technique in the presence of hBMSCs after 7 and 14 days of treatment. Enhanced mineral deposition was observed in the composite scaffolds compared to the control, indicating superior composite mineralization potential. Upregulation of osteogenic-associated genes was observed in the scaffold-treated groups relative to the control, showing superior scaffold osteogenic potential. These results demonstrate that 3D-printed scaffolds are potential candidates for bone tissue engineering applications.