Quality control (QC) of structures segmentation in volumetric medical images is important for identifying segmentation errors in clinical practice and for facilitating model development by enhancing network performance in semi-supervised and active learning scenarios. This paper introduces SegQC, a novel framework for segmentation quality estimation and segmentation error detection. SegQC computes an estimate measure of the quality of a segmentation in volumetric scans and in their individual slices and identifies possible segmentation error regions within a slice. The key components of SegQC include: 1) SegQCNet, a deep network that inputs a scan and its segmentation mask and outputs segmentation error probabilities for each voxel in the scan; 2) three new segmentation quality metrics computed from the segmentation error probabilities; 3) a new method for detecting possible segmentation errors in scan slices computed from the segmentation error probabilities. We introduce a novel evaluation scheme to measure segmentation error discrepancies based on an expert radiologist’s corrections of automatically produced segmentations that yields smaller observer variability and is closer to actual segmentation errors. We demonstrate SegQC on three fetal structures in 198 fetal MRI scans – fetal brain, fetal body and the placenta. To assess the benefits of SegQC, we compare it to the unsupervised Test Time Augmentation (TTA)-based QC and to supervised autoencoder (AE)-based QC. Our studies indicate that SegQC outperforms TTA-based quality estimation for whole scans and individual slices in terms of Pearson correlation and MAE for fetal body and fetal brain structures segmentation as well as for volumetric overlap metrics estimation of the placenta structure. Compared to both unsupervised TTA and supervised AE methods, SegQC achieves lower MAE for both 3D and 2D Dice estimates and higher Pearson correlation for volumetric Dice. Our segmentation error detection method achieved recall and precision rates of 0.77 and 0.48 for fetal body, and 0.74 and 0.55 for fetal brain segmentation error detection, respectively. Ranking derived from metrics estimation surpasses rankings based on entropy and sum for TTA and SegQCNet estimations, respectively. SegQC provides high-quality metrics estimation for both 2D and 3D medical images as well as error localization within slices, offering important improvements to segmentation QC.