In this study, the activity of oxidative stress parameters superoxide dismutase (SOD), catalase (CAT), glutathione peroxidase (GSH-Px), glutathione reductase (GR), and glutathione S-transferase (GST), as well as the concentrations of vitamin E (Vit E) and SH groups in the digestive glands and gills of freshwater mussels Unio pictorum and Sinanodonta woodiana from the Sava River in Serbia were investigated. These parameters were determined in native and invasive mussels under the same environmental conditions. The activities of GSH-Px and GR and the concentration of Vit E were significantly higher in the digestive glands of the autochthonous species U. pictorum than in the invasive species S. woodiana, while the CAT activity and the concentration of SH groups were lower. In the gills of U. pictorum, GSH-Px activity and Vit E concentration were significantly higher, while CAT, GST, and SH groups were lower. Principal component analysis (PCA) showed that oxidative stress parameters were strictly tissue- and species-specific. In addition, integrated biomarker response (IBR) showed a combined response of enzymatic and non-enzymatic oxidative stress parameters depending on the tissue or species studied, indicating different metabolic activities and behaviors of an autochthonous versus an introduced bivalve species.