In time-lapse microscopy, inherent noise significantly limits imaging sensitivity and increases measurement uncertainty. Due to the scarcity of clean data, zero-shot approaches have emerged as highly data-efficient solutions for microscopy denoising. However, existing methods typically process video frames independently, resulting in long training times and issues such as temporal noise and over-smoothing. In this paper, we introduce MDSR-Zero, a zero-shot online learning method designed for plug-and-play noise suppression and super-resolution of microscopy videos. Our approach leverages an efficient online training strategy that reuses denoising models from previous frames. By treating the video as a continuous stream, our model significantly reduces training time and ensures temporally consistent denoising. Additionally, we propose a novel loss function tailored for denoising in the context of super-resolution, which enhances the detail in the denoised results. Extensive experiments on both synthetic and real-world noise demonstrate that our method achieves state-of-the-art performance among zero-shot denoising approaches and is competitive with self-supervised methods. Notably, our method can reduce training time by up to 10x compared to the previous SOTA method.