Volumetric magnetic resonance (MR) image segmentation plays an important role in many clinical applications. Deep learning (DL) has recently achieved state-of-the-art or even human-level performance on various image segmentation tasks. Nevertheless, manually annotating volumetric MR images for DL model training is labor-exhaustive and time-consuming. In this work, we aim to train a semi-supervised and self-supervised collaborative learning framework for prostate 3D MR image segmentation while using extremely sparse annotations, for which the ground truth annotations are provided for just the central slice of each volumetric MR image. Specifically, semi-supervised learning and self-supervised learning methods are used to generate two independent sets of pseudo labels. These pseudo labels are then fused by the Boolean operation to extract a more confident pseudo label set. The images with either manual or network self-generated labels are then employed to train a segmentation model for target volume extraction. Experimental results on a publicly available prostate MR image dataset demonstrate that, while requiring significantly less annotation effort, our framework generates very encouraging segmentation results. The proposed framework is very useful in clinical applications when training data with dense annotations are difficult to obtain.