Nitrosative stress promotes protein glycoxidation, and both processes can occur during an infection with the SARS-CoV-2 virus. Therefore, the aim of this study was to assess selected nitrosative stress parameters and protein glycoxidation products in COVID-19 patients and convalescents relative to healthy subjects, including in reference to the severity of COVID-19 symptoms. The diagnostic utility of nitrosative stress and protein glycoxidation biomarkers was also evaluated in COVID-19 patients. The study involved 218 patients with COVID-19, 69 convalescents, and 48 healthy subjects. Nitrosative stress parameters (NO, S-nitrosothiols, nitrotyrosine) and protein glycoxidation products (tryptophan, kynurenine, N-formylkynurenine, dityrosine, AGEs) were measured in the blood plasma or serum with the use of colorimetric/fluorometric methods. The levels of NO (p = 0.0480), S-nitrosothiols (p = 0.0004), nitrotyrosine (p = 0.0175), kynurenine (p < 0.0001), N-formylkynurenine (p < 0.0001), dityrosine (p < 0.0001), and AGEs (p < 0.0001) were significantly higher, whereas tryptophan fluorescence was significantly (p < 0.0001) lower in COVID-19 patients than in the control group. Significant differences in the analyzed parameters were observed in different stages of COVID-19. In turn, the concentrations of kynurenine (p < 0.0001), N-formylkynurenine (p < 0.0001), dityrosine (p < 0.0001), and AGEs (p < 0.0001) were significantly higher, whereas tryptophan levels were significantly (p < 0.0001) lower in convalescents than in healthy controls. The ROC analysis revealed that protein glycoxidation products can be useful for diagnosing infections with the SARS-CoV-2 virus because they differentiate COVID-19 patients (KN: sensitivity—91.20%, specificity—92.00%; NFK: sensitivity—92.37%, specificity—92.00%; AGEs: sensitivity—99,02%, specificity—100%) and convalescents (KN: sensitivity—82.22%, specificity—84.00%; NFK: sensitivity—82,86%, specificity—86,00%; DT: sensitivity—100%, specificity—100%; AGE: sensitivity—100%, specificity—100%) from healthy subjects with high sensitivity and specificity. Nitrosative stress and protein glycoxidation are intensified both during and after an infection with the SARS-CoV-2 virus. The levels of redox biomarkers fluctuate in different stages of the disease. Circulating biomarkers of nitrosative stress/protein glycoxidation have potential diagnostic utility in both COVID-19 patients and convalescents.