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In this work, we introduce a method for automatic renal compartment segmentation from Dynamic Contrast-Enhanced MRI (DCE-MRI) images, which is an important problem but existing solutions cannot achieve high accuracy robustly for a wide range of data. The proposed method consists of three main steps. First, the whole kidney is segmented based on the concept of Maximally Stable Temporal Volume (MSTV). The proposed MSTV detects anatomical structures that are stable in both spatial domain and temporal dynamics. MSTV-based kidney segmentation is robust to noises and does not require a training phase. It can well adapt to kidney shape variations caused by renal dysfunction. Second, voxels in the segmented kidney are described by principal components (PCs) to remove temporal redundancy and noises. And then k-means clustering of PCs is applied to separate voxels into cortex, medulla and pelvis. Third, a refinement method is introduced to further remove noises in each segmented compartment. Experimental results on 16 clinical kidney datasets demonstrate that our method reaches a very high level of agreement with manual results and achieves superior performance to three existing baseline methods. The source code of the proposed method will be made publicly available with the publication of this paper.