Masked autoencoders (MAE) have shown great promise in medical image classification. However, the random masking strategy employed by traditional MAEs may overlook critical areas in medical images, where even subtle changes can indicate disease. To address this limitation, we propose a novel approach that utilizes a multifractal measure (Renyi entropy) to optimize the masking strategy. Our method, termed Multifractal-Optimized Masked Autoencoder (MO-MAE), employs a multifractal analysis to identify regions of high complexity and information content. By focusing the masking process on these areas, MO-MAE ensures that the model learns to reconstruct the most diagnostically relevant features. This approach is particularly beneficial for medical imaging, where fine-grained inspection of tissue structures is crucial for accurate diagnosis. We evaluate MO-MAE on several medical datasets covering various diseases, including MedMNIST and COVID-CT. Our results demonstrate that MO-MAE achieves promising performance, surpassing other basiline and state-of-the-art models. The proposed method also adds minimum computational overhead as the computation of the proposed measure is straightforward. Our findings suggest that the multifractal-optimized masking strategy enhances the model's ability to capture and reconstruct complex tissue structures, leading to more accurate and efficient medical image representation. The proposed MO-MAE framework offers a promising direction for improving the accuracy and efficiency of deep learning models in medical image analysis, potentially advancing the field of computer-aided diagnosis.