Since December 2019, the world has been intensely affected by the COVID-19 pandemic, caused by the SARS-CoV-2. In the case of a novel virus identification, the early elucidation of taxonomic classification and origin of the virus genomic sequence is essential for strategic planning, containment, and treatments. Deep learning techniques have been successfully used in many viral classification problems associated with viral infection diagnosis, metagenomics, phylogenetics, and analysis. Considering that motivation, the authors proposed an efficient viral genome classifier for the SARS-CoV-2 using the deep neural network based on the stacked sparse autoencoder (SSAE). For the best performance of the model, we explored the utilization of image representations of the complete genome sequences as the SSAE input to provide a classification of the SARS-CoV-2. For that, a dataset based on k-mers image representation was applied. We performed four experiments to provide different levels of taxonomic classification of the SARS-CoV-2. The SSAE technique provided great performance results in all experiments, achieving classification accuracy between 92% and 100% for the validation set and between 98.9% and 100% when the SARS-CoV-2 samples were applied for the test set. In this work, samples of the SARS-CoV-2 were not used during the training process, only during subsequent tests, in which the model was able to infer the correct classification of the samples in the vast majority of cases. This indicates that our model can be adapted to classify other emerging viruses. Finally, the results indicated the applicability of this deep learning technique in genome classification problems.