Nanocomposite hydrogels based on carbon nanotubes (CNTs) are known to possess remarkable stiffness, electrical, and thermal conductivity. However, they often make use of CNTs as fillers in covalently cross-linked hydrogel networks or involve direct cross-linking between CNTs and polymer chains, limiting processability properties. Herein, nanocomposite hydrogels are developed, in which CNTs are fillers in a physically cross-linked hydrogel. Supramolecular nanocomposites are prepared at various CNT concentrations, ranging from 0.5 to 6 wt%. Incorporation of 3 wt% of CNTs leads to an increase of the material’s toughness by over 80%, and it enhances electrical conductivity by 358%, compared to CNT-free hydrogel. Meanwhile, the nanocomposite hydrogels maintain thixotropy and processability, typical of the parent hydrogel. The study also demonstrates that these materials display remarkable cytocompatibility and support cell growth and proliferation, while preserving their functional activities. These supramolecular nanocomposite hydrogels are therefore promising candidates for biomedical applications, in which both toughness and electrical conductivity are important parameters.