Supramolecular hydrogels (SMHs) are three-dimensional constructs wherein the majority of the volume is occupied by water. Since the bonding forces between the components of SMHs are noncovalent, SMH properties are often tunable, stimuli-responsive, and reversible, which enables applications including triggered drug release, sensing, and tissue engineering. Meanwhile, single-walled carbon nanotubes (SWCNTs) possess superlative electrical and thermal conductivities, high mechanical strength, and strong optical absorption at near-infrared wavelengths that have the potential to add unique functionality to SMHs. However, SWCNT-based SMHs have thus far not realized the potential of the optical properties of SWCNTs to enable reversible response to near-infrared irradiation. Here, we present a novel SMH architecture comprised solely of DNA and SWCNTs, wherein noncovalent interactions provide structural integrity without compromising the intrinsic properties of SWCNTs. The mechanical properties of these SMHs are readily tuned by varying the relative concentrations of DNA and SWCNTs, which varies the cross-linking density as shown by molecular dynamics simulations. Moreover, the SMH gelation transition is fully reversible and can be triggered by a change in temperature or near-infrared irradiation. This work explores a new regime for SMHs with potential utility for a range of applications including sensors, actuators, responsive substrates, and 3D printing.