Visible watermark removal is challenging due to its inherent complexities and the noise carried within images. Existing methods primarily rely on supervised learning approaches that require paired datasets of watermarked and watermark-free images, which are often impractical to obtain in real-world scenarios. To address this challenge, we propose SSH-Net, a Self-Supervised and Hybrid Network specifically designed for noisy image watermark removal. SSH-Net synthesizes reference watermark-free images using the watermark distribution in a self-supervised manner and adopts a dual-network design to address the task. The upper network, focused on the simpler task of noise removal, employs a lightweight CNN-based architecture, while the lower network, designed to handle the more complex task of simultaneously removing watermarks and noise, incorporates Transformer blocks to model long-range dependencies and capture intricate image features. To enhance the model's effectiveness, a shared CNN-based feature encoder is introduced before dual networks to extract common features that both networks can leverage. Our code will be available at https://github.com/wenyang001/SSH-Net.