Ammonia leaching is a promising method for processing low-grade copper ores, especially those containing large amounts of oxidized copper. In this paper, we study the effect of Si-containing minerals on the kinetics of Cu and Ag leaching from low-grade copper concentrates. The results of experiments on the pressure leaching of the initial copper concentrate in an ammonium/ammonium-carbonate solution with oxygen as an oxidizing agent are in good agreement with the shrinking core model in the intra-diffusion mode: in this case, the activation energies were 53.50 kJ/mol for Cu and 90.35 kJ/mol for Ag. Energy-dispersive X-ray spectroscopy analysis (EDX) analysis showed that reagent diffusion to Cu-bearing minerals can be limited by aluminosilicate minerals of the gangue. The recovery rate for copper and silver increases significantly after a preliminary alkaline desilication of the concentrate, and the new shrinking core model is the most adequate, showing that the process is limited by diffusion through the product layer and interfacial diffusion. The activation energy of the process increases to 86.76 kJ/mol for Cu and 92.15 kJ/mol for Ag. Using the time-to-a-given-fraction method, it has been shown that a high activation energy is required in the later stages of the process, when the most resistant sulfide minerals of copper and silver apparently remain.