The recent Segment Anything Model (SAM) is a significant advancement in natural image segmentation, exhibiting potent zero-shot performance suitable for various downstream image segmentation tasks. However, directly utilizing the pretrained SAM for Infrared Small Target Detection (IRSTD) task falls short in achieving satisfying performance due to a notable domain gap between natural and infrared images. Unlike a visible light camera, a thermal imager reveals an object's temperature distribution by capturing infrared radiation. Small targets often show a subtle temperature transition at the object's boundaries. To address this issue, we propose the IRSAM model for IRSTD, which improves SAM's encoder-decoder architecture to learn better feature representation of infrared small objects. Specifically, we design a Perona-Malik diffusion (PMD)-based block and incorporate it into multiple levels of SAM's encoder to help it capture essential structural features while suppressing noise. Additionally, we devise a Granularity-Aware Decoder (GAD) to fuse the multi-granularity feature from the encoder to capture structural information that may be lost in long-distance modeling. Extensive experiments on the public datasets, including NUAA-SIRST, NUDT-SIRST, and IRSTD-1K, validate the design choice of IRSAM and its significant superiority over representative state-of-the-art methods. The source code will be released.