Diffusion-weighted Magnetic Resonance Imaging (dMRI) is increasingly used to study the fetal brain in utero. An important computation enabled by dMRI is streamline tractography, which has unique applications such as tract-specific analysis of the brain white matter and structural connectivity assessment. However, due to the low fetal dMRI data quality and the challenging nature of tractography, existing methods tend to produce highly inaccurate results. They generate many false streamlines while failing to reconstruct streamlines that constitute the major white matter tracts. In this paper, we advocate for anatomically constrained tractography based on an accurate segmentation of the fetal brain tissue directly in the dMRI space. We develop a deep learning method to compute the segmentation automatically. Experiments on independent test data show that this method can accurately segment the fetal brain tissue and drastically improve tractography results. It enables the reconstruction of highly curved tracts such as optic radiations. Importantly, our method infers the tissue segmentation and streamline propagation direction from a diffusion tensor fit to the dMRI data, making it applicable to routine fetal dMRI scans. The proposed method can lead to significant improvements in the accuracy and reproducibility of quantitative assessment of the fetal brain with dMRI.