The magnetic resonance (MR) imaging technique is widely used in clinical diagnosis. Unfortunately, in practice, the MR images inevitably suffer from noise, which severely degrades image quality and accordingly impacts on the accuracy of clinical diagnosis. By exploiting both the nonlocal similarity over space and the inherent correlation across the slices of the 3D MR images, in this paper, we present a novel Rician noise reduction method for the 3D MR images. Specifically, the 3D nonlocal similar patches are first extracted from the input noisy 3D MR data and then grouped to form a noisy fourth-order tensor. Since 3D patches used to construct the fourth-order tensor share similar structures, a latent noise-free tensor can be approximated by a low-rank tensor. To this end, the higher-order singular value decomposition (HOSVD) is adopted to recover the latent noise-free tensor. Furthermore, the rank of each mode of the tensor is adaptively determined by an enhanced low-rank method. The experimental results on synthetic and real 3D MR images show that the proposed method outperforms several state-of-the-art denoising methods in terms of objective metrics and visual inspection.