Structural reconstruction of plant roots from MRI is challenging, because of low resolution and low signal-to-noise ratio of the 3D measurements which may lead to disconnectivities and wrongly connected roots. We propose a two-stage approach for this task. The first stage is based on semantic root vs. soil segmentation and finds lowest-cost paths from any root voxel to the shoot. The second stage takes the largest fully connected component generated in the first stage and uses 3D skeletonization to extract a graph structure. We evaluate our method on 22 MRI scans and compare to human expert reconstructions.