Chicory (Cichorium intybus L.) is a widely used nutritional and medicinal plant, whose roots are an important commercial source of inulin, while the aerial parts are often discarded during industrial processing. This study systematically compared chicory polysaccharides (CPs) extracted from aerial parts (CP-A) and roots (CP-R) with respect to their compositional features and cytoprotective effects in an oxygen–glucose deprivation/reperfusion (OGD/R)-induced H9c2 cell injury model. CP-A and CP-R differed in molecular weight distribution and monosaccharide composition, with CP-R exhibiting a higher molecular weight and fructose content. Despite these differences, both fractions significantly improved cell viability and reduced oxidative and biochemical injury markers. Integrated proteomic and transcriptomic analyses indicated that CP-A and CP-R were associated with the modulation of stress-responsive signaling networks, prominently involving oxidative stress-linked MAPK/NF-κB pathways. These findings demonstrate comparable cytoprotective activities of polysaccharide-rich fractions from roots and aerial parts and support the valorization of chicory aerial biomass as a potential source of functional ingredients for cardiovascular health.