In this study, the preparation of porous nanocomposite scaffolds (HX-CNT) from a combination of a hydroxamic derivative of alginate (HX) and an amine-functionalized multiwalled carbon nanotube (CNT) at different concentrations is described. The structure of HX was investigated by FTIR, and the degree of substitution around 9% was confirmed by elemental analysis. The interaction between CNT and alginate derivative in the nanocomposite crosslinked with calcium was confirmed by FTIR, Raman spectroscopy, and SEM. The results obtained in this study showed that scaffolds based on HX-CNT composites with a 4 wt% concentration level exhibited improved physical and mechanical properties compared to plain alginate (Young’s modulus increased from 2.2 to 5.1 MPa and elastic strength from 0.13 to 0.25 MPa) and decreased the swelling ratios from ~900 to ~673. The cytotoxicity assays using the L929 cell line proved that the nanocomposite scaffolds were nontoxic, even at the highest CNT concentration.