Speech Super-Resolution (SSR) is a task of enhancing low-resolution speech signals by restoring missing high-frequency components. Conventional approaches typically reconstruct log-mel features, followed by a vocoder that generates high-resolution speech in the waveform domain. However, as mel features lack phase information, this can result in performance degradation during the reconstruction phase. Motivated by recent advances with Selective State Spaces Models (SSMs), we propose a method, referred to as Wave-U-Mamba that directly performs SSR in time domain. In our comparative study, including models such as WSRGlow, NU-Wave 2, and AudioSR, Wave-U-Mamba demonstrates superior performance, achieving the lowest Log-Spectral Distance (LSD) across various low-resolution sampling rates, ranging from 8 to 24 kHz. Additionally, subjective human evaluations, scored using Mean Opinion Score (MOS) reveal that our method produces SSR with natural and human-like quality. Furthermore, Wave-U-Mamba achieves these results while generating high-resolution speech over nine times faster than baseline models on a single A100 GPU, with parameter sizes less than 2\% of those in the baseline models.