In this study, the intrinsic surface-enhanced Raman spectroscopy (SERS)-based approach coupled with chemometric analysis was adopted to establish the biochemical fingerprint of SARS-CoV-2 infected human fluids: saliva and nasopharyngeal swabs. The numerical methods, partial least squares discriminant analysis (PLS-DA) and support vector machine classification (SVMC), facilitated the spectroscopic identification of the viral-specific molecules, molecular changes, and distinct physiological signatures of pathetically altered fluids. Next, we developed the reliable classification model for fast identification and differentiation of negative CoV(−) and positive CoV(+) groups. The PLS-DA calibration model was described by a great statistical value—RMSEC and RMSECV below 0.3 and R2cal at the level of ~0.7 for both type of body fluids. The calculated diagnostic parameters for SVMC and PLS-DA at the stage of preparation of calibration model and classification of external samples simulating real diagnostic conditions evinced high accuracy, sensitivity, and specificity for saliva specimens. Here, we outlined the significant role of neopterin as the biomarker in the prediction of COVID-19 infection from nasopharyngeal swab. We also observed the increased content of nucleic acids of DNA/RNA and proteins such as ferritin as well as specific immunoglobulins. The developed SERS for SARS-CoV-2 approach allows: (i) fast, simple and non-invasive collection of analyzed specimens; (ii) fast response with the time of analysis below 15 min, and (iii) sensitive and reliable SERS-based screening of COVID-19 disease.