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Fetal brain segmentation is an important first step for slice-level motion correction and slice-to-volume reconstruction in fetal MRI. Fast and accurate segmentation of the fetal brain on fetal MRI is required to achieve real-time fetal head pose estimation and motion tracking for slice re-acquisition and steering. To address this critical unmet need, in this work we analyzed the speed-accuracy performance of a variety of deep neural network models, and devised a symbolically small convolutional neural network that combines spatial details at high resolution with context features extracted at lower resolutions. We used multiple branches with skip connections to maintain high accuracy while devising a parallel combination of convolution and pooling operations as an input downsampling module to further reduce inference time. We trained our model as well as eight alternative, state-of-the-art networks with manually-labeled fetal brain MRI slices and tested on two sets of normal and challenging test cases. Experimental results show that our network achieved the highest accuracy and lowest inference time among all of the compared state-of-the-art real-time segmentation methods. We achieved average Dice scores of 97.99\% and 84.04\% on the normal and challenging test sets, respectively, with an inference time of 3.36 milliseconds per image on an NVIDIA GeForce RTX 2080 Ti. Code, data, and the trained models are available at https://github.com/bchimagine/real_time_fetal_brain_segmentation.