Early identification of epidermal growth factor receptor (EGFR) and Kirsten rat sarcoma viral oncogene homolog (KRAS) mutations is crucial for selecting a therapeutic strategy for patients with non-small-cell lung cancer (NSCLC). We proposed a machine learning-based model for feature selection and prediction of EGFR and KRAS mutations in patients with NSCLC by including the least number of the most semantic radiomics features. We included a cohort of 161 patients from 211 patients with NSCLC from The Cancer Imaging Archive (TCIA) and analyzed 161 low-dose computed tomography (LDCT) images for detecting EGFR and KRAS mutations. A total of 851 radiomics features, which were classified into 9 categories, were obtained through manual segmentation and radiomics feature extraction from LDCT. We evaluated our models using a validation set consisting of 18 patients derived from the same TCIA dataset. The results showed that the genetic algorithm plus XGBoost classifier exhibited the most favorable performance, with an accuracy of 0.836 and 0.86 for detecting EGFR and KRAS mutations, respectively. We demonstrated that a noninvasive machine learning-based model including the least number of the most semantic radiomics signatures could robustly predict EGFR and KRAS mutations in patients with NSCLC.