Bone mineral density (BMD) is the international standard for evaluating osteoporosis/osteopenia. The success rate of BMD alone in estimating the risk of vertebral fragility fracture (VFF) is approximately 50%, making BMD far from ideal in predicting VFF. In addition, whether or not a patient has been diagnosed with osteoporosis or osteopenia, he or she may suffer a VFF. For this reason, we conducted an extensive empirical study to assess VFFs in postmenopausal women. We considered a representative dataset of 94 T1- and T2-weighted routine spine MRI (with osteopenia or osteoporosis), split into 2,400 samples (slices). Comparing the classification results of machine learning and deep learning (DL) techniques showed that DL generally achieved better results at the cost of higher computational power and hard explainability. ResNet achieved the best results in discriminating patients from groups with and without VFFs with 83% accuracy and 90% AUC (with a confidence interval of 99%). Our results represent a significant step toward prospective and longitudinal studies investigating methods to achieve higher accuracy in predicting VFFs based on spine MRI features of vertebrae without fracture.