A redox-responsive nanocarrier is a promising strategy for the intracellular drug release because it protects the payload, prevents its undesirable leakage during extracellular transport, and favors site-specific drug delivery. In this study, we developed a novel redox responsive core-shell structure nanohydrogel prepared by a water in oil nanoemulsion method using two biocompatible synthetic polymers: vinyl sulfonated poly(N-(2-hydroxypropyl) methacrylamide mono/dilactate)-polyethylene glycol-poly(N-(2-hydroxypropyl) methacrylamide mono/dilactate) triblock copolymer, and thiolated hyaluronic acid. The influence on the nanohydrogel particle size and distribution of formulation parameters was investigated by a three-level full factorial design to optimize the preparation conditions. The surface and core-shell morphology of the nanohydrogel were observed by scanning electron microscope, transmission electron microscopy, and further confirmed by Fourier transform infrared spectroscopy and Raman spectroscopy from the standpoint of chemical composition. The redox-responsive biodegradability of the nanohydrogel in reducing environments was determined using glutathione as reducing agent. A nanohydrogel with particle size around 250 nm and polydispersity index around 0.1 is characterized by a thermosensitive shell which jellifies at body temperature and crosslinks at the interface of a redox-responsive hyaluronic acid core via the Michael addition reaction. The nanohydrogel showed good encapsulation efficiency for model macromolecules of different molecular weight (93% for cytochrome C, 47% for horseradish peroxidase, and 90% for bovine serum albumin), capacity to retain the peroxidase-like enzymatic activity (around 90%) of cytochrome C and horseradish peroxidase, and specific redox-responsive release behavior. Additionally, the nanohydrogel exhibited excellent cytocompatibility and internalization efficiency into macrophages. Therefore, the developed core-shell structure nanohydrogel can be considered a promising tool for the potential intracellular delivery of different pharmaceutical applications, including for cancer therapy.