Exploiting temporal correlations is crucial for video super-resolution (VSR). Recent approaches enhance this by incorporating event cameras. In this paper, we introduce MamEVSR, an Mamba-based network for event-based VSR that leverages the selective state space model, Mamba. MamEVSR stands out by offering global receptive field coverage with linear computational complexity, thus addressing the limitations of convolutional neural networks and Transformers. The key components of MamEVSR include: (1) The interleaved Mamba (iMamba) block, which interleaves tokens from adjacent frames and applies multi-directional selective state space modeling, enabling efficient feature fusion and propagation across bi-directional frames while maintaining linear complexity. (2) The cross-modality Mamba (cMamba) block facilitates further interaction and aggregation between event information and the output from the iMamba block. The cMamba block can leverage complementary spatio-temporal information from both modalities and allows MamEVSR to capture finer motion details. Experimental results show that the proposed MamEVSR achieves superior performance on various datasets quantitatively and qualitatively.