Deep neural networks have significantly improved volumetric medical segmentation, but they generally require large-scale annotated data to achieve better performance, which can be expensive and prohibitive to obtain. To address this limitation, existing works typically perform transfer learning or design dedicated pretraining-finetuning stages to learn representative features. However, the mismatch between the source and target domain can make it challenging to learn optimal representation for volumetric data, while the multi-stage training demands higher compute as well as careful selection of stage-specific design choices. In contrast, we propose a universal training framework called MedContext that is architecture-agnostic and can be incorporated into any existing training framework for 3D medical segmentation. Our approach effectively learns self-supervised contextual cues jointly with the supervised voxel segmentation task without requiring large-scale annotated volumetric medical data or dedicated pretraining-finetuning stages. The proposed approach induces contextual knowledge in the network by learning to reconstruct the missing organ or parts of an organ in the output segmentation space. The effectiveness of MedContext is validated across multiple 3D medical datasets and four state-of-the-art model architectures. Our approach demonstrates consistent gains in segmentation performance across datasets and architectures even in fewshot scenarios. Our code is available at https://github.com/hananshafi/medcontext.