The coronavirus disease 2019 (COVID-19), as a severe respiratory disease, affects many parts of the body, and approximately 20–85% of patients exhibit functional impairment of the senses of smell and taste, some of whom even experience the permanent loss of these senses. These symptoms are not life-threatening but severely affect patients’ quality of life and increase the risk of depression and anxiety. The pathological mechanisms of these symptoms have not been fully identified. In the current study, we aimed to identify the important biomarkers at the expression level associated with the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection-mediated loss of taste or olfactory ability, and we have suggested the potential pathogenetic mechanisms of COVID-19 complications. We designed a machine-learning-based approach to analyze the transcriptome of 577 COVID-19 patient samples, including 84 COVID-19 samples with a decreased ability to taste or smell and 493 COVID-19 samples without impairment. Each sample was represented by 58,929 gene expression levels. The features were analyzed and sorted by three feature selection methods (least absolute shrinkage and selection operator, light gradient boosting machine, and Monte Carlo feature selection). The optimal feature sets were obtained through incremental feature selection using two classification algorithms: decision tree (DT) and random forest (RF). The top genes identified by these multiple methods (H3-5, NUDT5, and AOC1) are involved in olfactory and gustatory impairments. Meanwhile, a high-performance RF classifier was developed in this study, and three sets of quantitative rules that describe the impairment of olfactory and gustatory functions were obtained based on the optimal DT classifiers. In summary, this study provides a new computation analysis and suggests the latent biomarkers (genes and rules) for predicting olfactory and gustatory impairment caused by COVID-19 complications.