The evolution of the neutralization reaction in a stationary droplet of cylindrical shape, extracting a surfactant from the surrounding mixture in a vertical Hele-Shaw cell, was studied experimentally. In our experiment, we used a new method of the simultaneous visualization of the refractive index field of light and the distribution of acidity levels in the solutions of source reactants and reaction products within the droplet. To carry out this approach, we utilized a Fizeau interferometer and added a pH indicator to the droplet before the experiment. A digital video camera recorded the resulting interference pattern with the superimposed color distribution created by solutions with different acidity levels. The study was conducted on a system of liquids where the chemical potentials would be equal when the concentration of the extracted reactant in the droplet was much higher than in the surrounding environment. Two variants of reaction realization—with and without Marangoni convection development—were considered. We determined the structures of flows and concentration fields in the droplet and its neighborhood and traced their evolution. Also, we evaluated the characteristic times of the extraction process depending on the initial reactant concentrations and droplet sizes. It was found that the resulting Marangoni convection had an oscillatory character and continued after the reaction completion. As expected, the formation of the capillary motion intensified the progression of chemical reaction inside the droplet.