Thyroid disease prediction has emerged as an important task recently. Despite existing approaches for its diagnosis, often the target is binary classification, the used datasets are small-sized and results are not validated either. Predominantly, existing approaches focus on model optimization and the feature engineering part is less investigated. To overcome these limitations, this study presents an approach that investigates feature engineering for machine learning and deep learning models. Forward feature selection, backward feature elimination, bidirectional feature elimination, and machine learning-based feature selection using extra tree classifiers are adopted. The proposed approach can predict Hashimoto’s thyroiditis (primary hypothyroid), binding protein (increased binding protein), autoimmune thyroiditis (compensated hypothyroid), and non-thyroidal syndrome (NTIS) (concurrent non-thyroidal illness). Extensive experiments show that the extra tree classifier-based selected feature yields the best results with 0.99 accuracy and an F1 score when used with the random forest classifier. Results suggest that the machine learning models are a better choice for thyroid disease detection regarding the provided accuracy and the computational complexity. K-fold cross-validation and performance comparison with existing studies corroborate the superior performance of the proposed approach.