Myocardial infarction (MI) causes rapid and permanent damage to the heart muscle. Without timely diagnosis and treatment, it will deteriorate the myocardial structure and function. The precise localization of MI based on 12-lead electrocardiogram (ECG) signals still remains a great challenge. We, thus, present a novel algorithm for automatically localizing MI from multilead ECG signals. The image-based heartbeat tensorization establishes a third-order lead x time x amplitude tensor structure. This image tensor encompasses key information between leads and the correlation within the heartbeat, which are essential for the MI diagnosis. The Tucker2 decomposition-based feature extractor automatically extracts the morphological core tensor of the image tensor. The morphological core tensor includes crucial information among three dimensions. Localization of MI is evaluated as a multiclass problem. We use the bagged decision tree for multiclass classification. The 12-lead ECG signals from the benchmark Physikalisch-Technische Bundesanstalt (PTB) database are employed to verify the applicability of the proposed algorithm. The PTB database includes normal ECG, 11 types of MI: anterior, anterior lateral, anterior septal, anterior septal lateral, inferior, inferior lateral, inferior posterior, inferior posterior lateral, lateral, posterior, and posterior lateral. We demonstrated, with the morphological core features obtained from the image tensor, that 12 categories of ECG signals achieved a total accuracy of 99.67% and an F1 score of 0.9997. The area under the receiver operating characteristic curves and precision-recall curves of each kind of ECG signal has been found to be more than 0.88. The proposed algorithm effectively realizes the classification of normal ECG and 11 categories of MI, and our approach of using a 12-lead ECG signal herein holds great promise for helping the cardiologists localize MI.