With the continuous advancement of deep learning technology, U-Net–based algorithms for image denoising play a crucial role in medical image processing. However, most U-Net-based medical image denoising algorithms typically have large parameter sizes, which poses significant limitations in practical applications where computational resources are limited or large-scale patient data processing are required. In this paper, we propose a medical image denoising algorithm called AsymUNet, developed using an asymmetric U-Net framework and a spatially rearranged multilayer perceptron (MLP). AsymUNet utilizes an asymmetric U-Net to reduce the computational burden, while a multiscale feature fusion module enhances the feature interaction between the encoder and decoder. To better preserve the image details, spatially rearranged MLP blocks serve as the core building blocks of AsymUNet. These blocks effectively extract both the local and global features of the image, reducing the model’s reliance on prior knowledge of the image and further accelerating the training and inference processes. Experimental results demonstrate that AsymUNet achieves superior performance metrics and visual results compared with other state-of-the-art methods.