This research work studies the self-healing ability, mechanical properties, and shape memory of the polymer Surlyn(®) 8940 with and without multiwall carbon nanotubes (MWCNTs) as a nanoreinforcement. This polymer comes from a partially neutralized poly(ethylene-co-methacrylic acid) (EMAA) ionomer copolymer. MWCNTs and the polymer went through a mixing process aimed at achieving an excellent dispersion. Later, an optimized extrusion method was used to produce a uniform reinforced filament, which was the input for the 3D-printing process that was used to create the final test samples. Various concentrations of MWCNTs (0.0, 0.1, 0.5, and 1.0 wt.%) were used to evaluate and compare the mechanical properties, self-healing ability, and shape memory of unreinforced and nanoreinforced materials. Results show an enhancement of the mechanical properties and self-healing ability through the addition of MWCNTs to the matrix of polymer, and the specimens showed shape memory events.