Age-related macular degeneration (AMD) is a leading cause of irreversible vision loss, making effective prognosis crucial for timely intervention. In this work, we propose AMD-Mamba, a novel multi-modal framework for AMD prognosis, and further develop a new AMD biomarker. This framework integrates color fundus images with genetic variants and socio-demographic variables. At its core, AMD-Mamba introduces an innovative metric learning strategy that leverages AMD severity scale score as prior knowledge. This strategy allows the model to learn richer feature representations by aligning learned features with clinical phenotypes, thereby improving the capability of conventional prognosis methods in capturing disease progression patterns. In addition, unlike existing models that use traditional CNN backbones and focus primarily on local information, such as the presence of drusen, AMD-Mamba applies Vision Mamba and simultaneously fuses local and long-range global information, such as vascular changes. Furthermore, we enhance prediction performance through multi-scale fusion, combining image information with clinical variables at different resolutions. We evaluate AMD-Mamba on the AREDS dataset, which includes 45,818 color fundus photographs, 52 genetic variants, and 3 socio-demographic variables from 2,741 subjects. Our experimental results demonstrate that our proposed biomarker is one of the most significant biomarkers for the progression of AMD. Notably, combining this biomarker with other existing variables yields promising improvements in detecting high-risk AMD patients at early stages. These findings highlight the potential of our multi-modal framework to facilitate more precise and proactive management of AMD.