Niobium, with its unique properties, plays a key role in high-tech industries, but its recovery from secondary sources remains poorly studied. The kinetics of niobium leaching from niobium-containing middlings obtained via the water treatment of dust chamber sublimations of titanium chlorinators is considered in this study. The leaching process was conducted using a fluoride–sulphuric acid solution. The experiments were performed at 25–90 °C in agitation mode. Kinetic data were analysed using compression-core and mixed-control models, which made it possible to establish the limiting stages of the process. A mixed mechanism, including a chemical reaction on the surface and diffusion through a layer of products with an activation energy of 30.05 kJ/mol, was established. The niobium recovery degree increased from 35.25 to 93.5% as the temperature increased, highlighting its effect on the process. The insoluble residue, rich in titanium, and the liquid phase with niobium and zirconium have the potential for further processing. The results provide the basis to optimise technologies intended to recover niobium from man-made raw materials, contributing to an increase in resource efficiency.