A combination of rheology and small-angle neutron scattering (SANS) experiments revealed the mechanism by which a surfactant can stiffen or soften physically cross-linked hydrogels. Here, the structure and rheological properties of a supramolecular hydrogel based on a random copolymer of N,N-dimethylacrylamide (DMA) and 2-(N-ethylperfluorooctane-sulfonamido)ethyl methacrylate (FOSM) were modified by the addition of sodium dodecyl sulfate (SDS). The effect of SDS concentration on the microstructure and properties of the hydrogel was determined by two types of experiments: (1) adding SDS by time-dependent, radial diffusion and (2) using samples where uniform loadings, i.e., no concentration gradient, of the SDS were achieved. Nanodomains consisting of FOSM aggregates were responsible for the physical cross-links in the hydrogel, but the formation of an equilibrium supramolecular network of the hydrogel was limited by conformational pinning of the water-swollen polymer segments by the relatively immobile FOSM groups within the nanodomains. The addition of low concentrations of SDS increased the equilibrium swelling of the hydrogel by as much as 3 times, but also increased the network cross-link density and the elastic modulus of the hydrogel. At sufficiently high SDS concentration, however, the surfactant effectively solvated the supramolecular bonds such that the nanodomain structure was partially destroyed, and the sample broke up into smaller pieces that eventually dissolved. The changes in the mechanical properties with addition of SDS corresponded to changes in the nanoscale morphology of the hydrogel measured by SANS.