Background: Segmentation of organs and structures in abdominal MRI is useful for many clinical applications, such as disease diagnosis and radiotherapy. Current approaches have focused on delineating a limited set of abdominal structures (13 types). To date, there is no publicly available abdominal MRI dataset with voxel-level annotations of multiple organs and structures. Consequently, a segmentation tool for multi-structure segmentation is also unavailable. Methods: We curated a T1-weighted abdominal MRI dataset consisting of 195 patients who underwent imaging at National Institutes of Health (NIH) Clinical Center. The dataset comprises of axial pre-contrast T1, arterial, venous, and delayed phases for each patient, thereby amounting to a total of 780 series (69,248 2D slices). Each series contains voxel-level annotations of 62 abdominal organs and structures. A 3D nnUNet model, dubbed as MRISegmentator-Abdomen (MRISegmentator in short), was trained on this dataset, and evaluation was conducted on an internal test set and two large external datasets: AMOS22 and Duke Liver. The predicted segmentations were compared against the ground-truth using the Dice Similarity Coefficient (DSC) and Normalized Surface Distance (NSD). Findings: MRISegmentator achieved an average DSC of 0.861$\pm$0.170 and a NSD of 0.924$\pm$0.163 in the internal test set. On the AMOS22 dataset, MRISegmentator attained an average DSC of 0.829$\pm$0.133 and a NSD of 0.908$\pm$0.067. For the Duke Liver dataset, an average DSC of 0.933$\pm$0.015 and a NSD of 0.929$\pm$0.021 was obtained. Interpretation: The proposed MRISegmentator provides automatic, accurate, and robust segmentations of 62 organs and structures in T1-weighted abdominal MRI sequences. The tool has the potential to accelerate research on various clinical topics, such as abnormality detection, radiotherapy, disease classification among others.