Segmentation of the uterine cavity and placenta in fetal magnetic resonance (MR) imaging is useful for the detection of abnormalities that affect maternal and fetal health. In this study, we used a fully convolutional neural network for 3D segmentation of the uterine cavity and placenta while a minimal operator interaction was incorporated for training and testing the network. The user interaction guided the network to localize the placenta more accurately. We trained the network with 70 training and 10 validation MRI cases and evaluated the algorithm segmentation performance using 20 cases. The average Dice similarity coefficient was 92% and 82% for the uterine cavity and placenta, respectively. The algorithm could estimate the volume of the uterine cavity and placenta with average errors of 2% and 9%, respectively. The results demonstrate that the deep learning-based segmentation and volume estimation is possible and can potentially be useful for clinical applications of human placental imaging.