In recent years, the exploitation of three-dimensional (3D) data in deep learning has gained momentum despite its inherent challenges. The necessity of 3D approaches arises from the limitations of two-dimensional (2D) techniques when applied to 3D data due to the lack of global context. A critical task in medical and microscopy 3D image analysis is instance segmentation, which is inherently complex due to the need for accurately identifying and segmenting multiple object instances in an image. Here, we introduce a 3D adaptation of the Mask R-CNN, a powerful end-to-end network designed for instance segmentation. Our implementation adapts a widely used 2D TensorFlow Mask R-CNN by developing custom TensorFlow operations for 3D Non-Max Suppression and 3D Crop And Resize, facilitating efficient training and inference on 3D data. We validate our 3D Mask R-CNN on two experiences. The first experience uses a controlled environment of synthetic data with instances exhibiting a wide range of anisotropy and noise. Our model achieves good results while illustrating the limit of the 3D Mask R-CNN for the noisiest objects. Second, applying it to real-world data involving cell instance segmentation during the morphogenesis of the ascidian embryo , we show that our 3D Mask R-CNN outperforms the state-of-the-art method, achieving high recall and precision scores. The model preserves cell connectivity, which is crucial for applications in quantitative study. Our implementation is open source, ensuring reproducibility and facilitating further research in 3D deep learning.