A promising strategy to design synthetic hydrogels with the ability to self-heal is to substitute the covalently cross-linked polymer chains by supramolecular ones. Although supramolecular hydrogels generally exhibit rapid self-healing without the need for any stimulus, they suffer from low mechanical strength which prevents them from any stress-bearing applications. Here, we describe a novel way for the production of self-healing hydrogels with shape memory behavior of high tensile strength (0.7-1.7 MPa) and stretch at break (800-900%). Hydrophobically modified poly(acrylic acid) (PAAc) chains with cetyltrimethylammonium (CTA) counterions form the physical network of such hydrogels. They were prepared via micellar copolymerization of acrylic acid with 2 mol % stearyl methacrylate (C18) as the hydrophobic comonomer in an aqueous NaBr solution of cetyltrimethylammonium bromide (CTAB). Extraction of free CTAB micelles from the physical gels results in a drastic increase in their Young's moduli (from 8-30 to 180-600 kPa) and tensile strengths (from 0.1-0.2 to 0.7-1.7 MPa) due to the complex formation between PAAc and CTAB. Loading and unloading cycles conducted on hydrogels both at the state of preparation and at equilibrium in water show a significant hysteresis and good superposition of the successive loading curves, demonstrating damage done during loading is recoverable in nature. The hydrogel samples self-healed via heating and surfactant treatment of the damaged areas withstand up to 1.5 MPa stresses and rupture at a stretch of 600%. Because of the drastic change in the elastic modulus of PAAc hydrogels with a change in temperature, they also exhibit shape memory properties with a recovery ratio of 100%.