Purpose: To develop a strategy for training a physics-guided MRI reconstruction neural network without a database of fully-sampled datasets. Theory and Methods: Self-supervised learning via data under-sampling (SSDU) for physics-guided deep learning (DL) reconstruction partitions available measurements into two disjoint sets, one of which is used in the data consistency units in the unrolled network and the other is used to define the loss for training. The proposed training without fully-sampled data is compared to fully-supervised training with ground-truth data, as well as conventional compressed sensing and parallel imaging methods using the publicly available fastMRI knee database. The same physics-guided neural network is used for both proposed SSDU and supervised training. The SSDU training is also applied to prospectively 2-fold accelerated high-resolution brain datasets at different acceleration rates, and compared to parallel imaging. Results: Results on five different knee sequences at acceleration rate of 4 shows that proposed self-supervised approach performs closely with supervised learning, while significantly outperforming conventional compressed sensing and parallel imaging, as characterized by quantitative metrics and a clinical reader study. The results on prospectively sub-sampled brain datasets, where supervised learning cannot be employed due to lack of ground-truth reference, show that the proposed self-supervised approach successfully perform reconstruction at high acceleration rates (4, 6 and 8). Image readings indicate improved visual reconstruction quality with the proposed approach compared to parallel imaging at acquisition acceleration. Conclusion: The proposed SSDU approach allows training of physics-guided DL-MRI reconstruction without fully-sampled data, while achieving comparable results with supervised DL-MRI trained on fully-sampled data.