Self-supervised masked image modeling has shown promising results on natural images. However, directly applying such methods to medical images remains challenging. This difficulty stems from the complexity and distinct characteristics of lesions compared to natural images, which impedes effective representation learning. Additionally, conventional high fixed masking ratios restrict reconstructing fine lesion details, limiting the scope of learnable information. To tackle these limitations, we propose a novel self-supervised medical image segmentation framework, Adaptive Masking Lesion Patches (AMLP). Specifically, we design a Masked Patch Selection (MPS) strategy to identify and focus learning on patches containing lesions. Lesion regions are scarce yet critical, making their precise reconstruction vital. To reduce misclassification of lesion and background patches caused by unsupervised clustering in MPS, we introduce an Attention Reconstruction Loss (ARL) to focus on hard-to-reconstruct patches likely depicting lesions. We further propose a Category Consistency Loss (CCL) to refine patch categorization based on reconstruction difficulty, strengthening distinction between lesions and background. Moreover, we develop an Adaptive Masking Ratio (AMR) strategy that gradually increases the masking ratio to expand reconstructible information and improve learning. Extensive experiments on two medical segmentation datasets demonstrate AMLP's superior performance compared to existing self-supervised approaches. The proposed strategies effectively address limitations in applying masked modeling to medical images, tailored to capturing fine lesion details vital for segmentation tasks.