Medical image fusion plays an important role in diagnosis and treatment of diseases such as image-guided radiotherapy and surgery. Although numerous medical image fusion methods have been proposed, most approaches have not touched the low rank nature of matrix formed by medical image, which usually lead to fusion image distortion and image information loss. These methods also often lack universality when dealing with different kinds of medical images. In this article, we propose a novel medical image fusion to overcome aforementioned issues on existing methods with the aid of low rank matrix approximation with nuclear norm minimization (NNM) constraint. The workflow of our method is described as: firstly, nonlocal similar patches across the medical image are searched by block matching for local patch in source images. Second, a fused matrix is stacking by shared nonlocal similarity patches, then the low rank matrix approximation methods under nuclear norm minimization can be used to recover low rank feature of fused matrix. Finally, fused image can be gotten by aggregating all the fused patches. Experimental results show that the proposed method is superior to other methods in both subjectively visual performance and objective criteria.