Agriculture, as the cornerstone of human civilization, constantly seeks to integrate technology for enhanced productivity and sustainability. This paper introduces $\textit{Agri-GNN}$, a novel Genotypic-Topological Graph Neural Network Framework tailored to capture the intricate spatial and genotypic interactions of crops, paving the way for optimized predictions of harvest yields. $\textit{Agri-GNN}$ constructs a Graph $\mathcal{G}$ that considers farming plots as nodes, and then methodically constructs edges between nodes based on spatial and genotypic similarity, allowing for the aggregation of node information through a genotypic-topological filter. Graph Neural Networks (GNN), by design, consider the relationships between data points, enabling them to efficiently model the interconnected agricultural ecosystem. By harnessing the power of GNNs, $\textit{Agri-GNN}$ encapsulates both local and global information from plants, considering their inherent connections based on spatial proximity and shared genotypes, allowing stronger predictions to be made than traditional Machine Learning architectures. $\textit{Agri-GNN}$ is built from the GraphSAGE architecture, because of its optimal calibration with large graphs, like those of farming plots and breeding experiments. $\textit{Agri-GNN}$ experiments, conducted on a comprehensive dataset of vegetation indices, time, genotype information, and location data, demonstrate that $\textit{Agri-GNN}$ achieves an $R^2 = .876$ in yield predictions for farming fields in Iowa. The results show significant improvement over the baselines and other work in the field. $\textit{Agri-GNN}$ represents a blueprint for using advanced graph-based neural architectures to predict crop yield, providing significant improvements over baselines in the field.