In this article, a leaching study, carried out on a quartz sample to obtain high-purity silica sands, has been presented. A leaching process by using oxalic acid to remove low iron content from the ore under study and to obtain a material suitable for fiber optic production has been evaluated. A characterization study has been carried out to establish the location of the iron impurities on the ore: 77 g/t was the maximum iron contamination, whereas, a final iron content <10 g/t (as Fe) has to be achieved for the application considered. The effect of the grinding process on the iron extraction yield has been established; the maximum iron extraction yield obtained with the ore as-is was about 45-50%, whereas extraction yields greater than 80-90% can be obtained after grinding the ore in different experimental conditions. An empirical model was evaluated to correlate the iron extraction yield obtained after 3 h of leaching at 80 °C, with 3 g/L of oxalic acid and 10% (w/v) of ore concentration, as a function of the average particle diameter of the ore after grinding. An iron extraction yield of about 98-100% can be obtained with an average particle diameter of about 20 µm. A schematic flowsheet of the process has been proposed considering the obtained experimental results and the results obtained in the literature for the waste treatment aspects. The experimental results have shown the technical feasibility of this process for the production of high-purity silica sands.