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UNet and its variations achieve state-of-the-art performances in medical image segmentation. In end-to-end learning, the training with high-resolution medical images achieves higher accuracy for medical image segmentation. However, the network depth, a massive number of parameters, and low receptive fields are issues in developing deep architecture. Moreover, the lack of multi-scale contextual information degrades the segmentation performance due to the different sizes and shapes of regions of interest. The extraction and aggregation of multi-scale features play an important role in improving medical image segmentation performance. This paper introduces the MH UNet, a multi-scale hierarchical-based architecture for medical image segmentation that addresses the challenges of heterogeneous organ segmentation. To reduce the training parameters and increase efficient gradient flow, we implement densely connected blocks. Residual-Inception blocks are used to obtain full contextual information. A hierarchical block is introduced between the encoder-decoder for acquiring and merging features to extract multi-scale information in the proposed architecture. We implement and validate our proposed architecture on four challenging MICCAI datasets. Our proposed approach achieves state-of-the-art performance on the BraTS 2018, 2019, and 2020 Magnetic Resonance Imaging (MRI) validation datasets. Our approach is 14.05 times lighter than the best method of BraTS 2018. In the meantime, our proposed approach has 2.2 times fewer training parameters than the top 3D approach on the ISLES 2018 Computed Tomographic Perfusion (CTP) testing dataset. MH UNet is available at https://github.com/parvezamu/MHUnet.