Electrocardiogram (ECG) is an important non-invasive method for diagnosing cardiovascular disease. However, ECG signals are susceptible to noise contamination, such as electrical interference or signal wandering, which reduces diagnostic accuracy. Various ECG denoising methods have been proposed, but most existing methods yield suboptimal performance under very noisy conditions or require several steps during inference, leading to latency during online processing. In this paper, we propose a novel ECG denoising model, namely Mamba-based ECG Enhancer (MECG-E), which leverages the Mamba architecture known for its fast inference and outstanding nonlinear mapping capabilities. Experimental results indicate that MECG-E surpasses several well-known existing models across multiple metrics under different noise conditions. Additionally, MECG-E requires less inference time than state-of-the-art diffusion-based ECG denoisers, demonstrating the model's functionality and efficiency.