Split Hopkinson pressure bar (SHPB) tests are usually used to determine the dynamic mechanical strength of basalt-fiber-reinforced concrete (BFRC), but this test method is time-consuming and expensive. This paper makes predictions about the dynamic mechanical strength of BFRC by employing machine learning (ML) algorithms and feature sets drawn from experimental data from prior works. However, there is still the problem of improving the accuracy of the dynamic mechanical strength prediction by the BFRC, which remains a challenge. Using stacking ensemble learning and genetic algorithms (GA) to optimize parameters, this study proposes a prediction method that combines these two techniques for obtaining accurate predictions. This method is composed of three parts: (1) the training uses multiple base learners, and the algorithms employed by the learners include extreme gradient boosting (XGBoost), gradient boosting (GB), random forest (RF), and support vector regression (SVR); (2) multi-base learners are combined using a stacking strategy to obtain the final prediction; and (3) using GA, the parameters are optimized in the prediction model. An experiment was conducted to compare the proposed approach with popular techniques for machine learning. In the study, the stacking ensemble algorithm integrated the base learner prediction results to improve the model’s performance and the GA further improved prediction accuracy. As a result of the application of the method, the dynamic mechanical strength of BFRC can be predicted with high accuracy. A SHAP analysis was also conducted using the stacking model to determine how important the contributing properties are and the sensitivity of the stacking model. Based on the results of this study, it was found that in the SHPB test, the strain rate had the most significant influence on the DIF, followed by the specimen diameter and the compressive strength.