The problem of liquid carbon dioxide injection into a formation containing methane hydrate, water and free methane is considered. Estimates of the main parameters show that the reaction of methane hydrate substitution by carbon dioxide hydrate without external heat influx is possible only in the presence of free water in the rock. Based on the analysis of the thermodynamic diagram of the phase state, a mathematical model of liquid CO2 injection accompanied by the reaction of methane substitution by carbon dioxide in the hydrate is formulated. It is assumed that the region of methane hydrate decomposition and carbon dioxide hydrate formation can be approximated by a narrow front. The found asymptotic solution reduces the problem to a numerical study of transcendental equations. Based on the results of numerical experiments, characteristic regimes of liquid carbon dioxide injection are presented, allowing the substitution reaction to occur.