Unmanned Aerial Vehicles (UAVs) have emerged as versatile tools across various sectors, driven by their mobility and adaptability. This paper introduces SkyVLN, a novel framework integrating vision-and-language navigation (VLN) with Nonlinear Model Predictive Control (NMPC) to enhance UAV autonomy in complex urban environments. Unlike traditional navigation methods, SkyVLN leverages Large Language Models (LLMs) to interpret natural language instructions and visual observations, enabling UAVs to navigate through dynamic 3D spaces with improved accuracy and robustness. We present a multimodal navigation agent equipped with a fine-grained spatial verbalizer and a history path memory mechanism. These components allow the UAV to disambiguate spatial contexts, handle ambiguous instructions, and backtrack when necessary. The framework also incorporates an NMPC module for dynamic obstacle avoidance, ensuring precise trajectory tracking and collision prevention. To validate our approach, we developed a high-fidelity 3D urban simulation environment using AirSim, featuring realistic imagery and dynamic urban elements. Extensive experiments demonstrate that SkyVLN significantly improves navigation success rates and efficiency, particularly in new and unseen environments.