To understand CO2 absorption into a basic solution saturated porous medium or a Hele-Shaw cell, the effect of the chemical reaction between dissolved CO2 and the basic reactant in the solution on the onset of a buoyancy-driven instability in a gas absorption process is analyzed theoretically. For the infinitely fast reaction, new linear and non-linear stability equations are derived without the quasi-steady state assumption (QSSA) and solved analytically. The present stability analysis without the QSSA shows that the important parameters are the dimensionless densification numbers and the reactant concentration ratio. For the physically unstable system, the chemical reaction can induce a non-monotonic density profile and has an important effect on the onset of instability motion. The effect of the reactant concentration ratio on the stability of the system is strongly dependent on the physical situation. Here, we call the system which is physically stable when there is no chemical reaction as the physically stable system. Even for this physically stable system, the chemical reaction makes the system unstable and induces the gravitational fingering instability motion. Also, it is found that the stability of the physically stable system is relatively insensitive to the non-monotonicity of the density profile.