Motion correction is a key element for imaging the fetal brain in-utero using Magnetic Resonance Imaging (MRI). Maternal breathing can introduce motion, but a larger effect is frequently due to fetal movement within the womb. Consequently, imaging is frequently performed slice-by-slice using single shot techniques, which are then combined into volumetric images using slice-to-volume reconstruction methods (SVR). For successful SVR, a key preprocessing step is to isolate fetal brain tissues from maternal anatomy before correcting for the motion of the fetal head. This has hitherto been a manual or semi-automatic procedure. We propose an automatic method to localize and segment the brain of the fetus when the image data is acquired as stacks of 2D slices with anatomy misaligned due to fetal motion. We combine this segmentation process with a robust motion correction method, enabling the segmentation to be refined as the reconstruction proceeds. The fetal brain localization process uses Maximally Stable Extremal Regions (MSER), which are classified using a Bag-of-Words model with Scale-Invariant Feature Transform (SIFT) features. The segmentation process is a patch-based propagation of the MSER regions selected during detection, combined with a Conditional Random Field (CRF). The gestational age (GA) is used to incorporate prior knowledge about the size and volume of the fetal brain into the detection and segmentation process. The method was tested in a ten-fold cross-validation experiment on 66 datasets of healthy fetuses whose GA ranged from 22 to 39 weeks. In 85% of the tested cases, our proposed method produced a motion corrected volume of a relevant quality for clinical diagnosis, thus removing the need for manually delineating the contours of the brain before motion correction. Our method automatically generated as a side-product a segmentation of the reconstructed fetal brain with a mean Dice score of 93%, which can be used for further processing.