Magnetic resonance imaging (MRI) is sensitive to Rician noise which degrades image quality and obscures critical anatomical details. We introduce a non-local wavelet UNet deep learning model developed to suppress Rician noise in \(T_1\) - and \(T_2\) -weighted MRI scans. Unlike conventional deep learning models designed under the assumption of Gaussian noise, our method is developed to address real noise present in MRI data during the acquisition process. We performed experiments on \(T_1\) - and \(T_2\) -weighted images with simulated noise levels (3%, 5%, 8% and 11%), real noisy diffusion-weighted images (DWI) and arterial spin labeling (ASL) images. By leveraging non-local similarity, wavelet transform and the UNet architecture, NLW-UNet demonstrates superior denoising capabilities in both quantitative and qualitative assessments. Notably, our model achieved the highest PSNR and SSIM across all evaluated test cases, outperforming state-of-the-art methods, including BM3D, DnCNN, FFDNet, SwinIR, EWT, and DRANet.