Sea surface temperature (SST) is an essential indicator of global climate change and one of the most intuitive factors reflecting ocean conditions. Obtaining high-resolution SST data remains challenging due to limitations in physical imaging, and super-resolution via deep neural networks is a promising solution. Recently, Mamba-based approaches leveraging State Space Models (SSM) have demonstrated significant potential for long-range dependency modeling with linear complexity. However, their application to SST data super-resolution remains largely unexplored. To this end, we propose the Wavelet-assisted Mamba Super-Resolution (WMSR) framework for satellite-derived SST data. The WMSR includes two key components: the Low-Frequency State Space Module (LFSSM) and High-Frequency Enhancement Module (HFEM). The LFSSM uses 2D-SSM to capture global information of the input data, and the robust global modeling capabilities of SSM are exploited to preserve the critical temperature information in the low-frequency component. The HFEM employs the pixel difference convolution to match and correct the high-frequency feature, achieving accurate and clear textures. Through comprehensive experiments on three SST datasets, our WMSR demonstrated superior performance over state-of-the-art methods. Our codes and datasets will be made publicly available at https://github.com/oucailab/WMSR.