Due to the continued evolution of the SARS-CoV-2 pandemic, researchers worldwide are working to mitigate, suppress its spread, and better understand it by deploying digital signal processing (DSP) and machine learning approaches. This study presents an alignment-free approach to classify the SARS-CoV-2 using complementary DNA, which is DNA synthesized from the single-stranded RNA virus. Herein, a total of 1582 samples, with different lengths of genome sequences from different regions, were collected from various data sources and divided into a SARS-CoV-2 and a non-SARS-CoV-2 group. We extracted eight biomarkers based on three-base periodicity, using DSP techniques, and ranked those based on a filter-based feature selection. The ranked biomarkers were fed into k-nearest neighbor, support vector machines, decision trees, and random forest classifiers for the classification of SARS-CoV-2 from other coronaviruses. The training dataset was used to test the performance of the classifiers based on accuracy and F-measure via 10-fold cross-validation. Kappa-scores were estimated to check the influence of unbalanced data. Further, 10x10 cross-validation paired t-test was utilized to test the best model with unseen data. Random forest was elected as the best model, differentiating the SARS-CoV-2 coronavirus from other coronaviruses and a control a group with an accuracy of 97.4%, sensitivity of 96.2%, and specificity of 98.2%, when tested with unseen samples. Moreover, the proposed algorithm was computationally efficient, taking only 0.31 seconds to compute the genome biomarkers, outperforming previous studies.