To understand the ${\mathrm{CO}}_2$ sequestration in the saline aquifer, the effect of a first-order chemical reaction on the onset of the buoyancy-driven instability in an isotropic reactive porous medium is analyzed theoretically. Under the linear stability theory, the stability equations are derived in the semi-infinite domain and they are solved with and without the quasi-steady-state approximation. We also considered the stability of the reactive system at a steady-state limit. The analysis for the steady-state case proposed that the onset of instability motion can occur during the transient period even if the system is stable at the steady state. Through the initial growth rate analysis the most unstable initial disturbance is determined, and it is found that initially the system is unconditionally stable regardless of the Damköhler number $D_a$ and the Darcy-Rayleigh number $\mathrm{Ra}$. Based on the results of the initial growth rate analysis, the direct numerical simulation is also conducted by using the Fourier pseudospectral method. The present theoretical and numerical analyses suggest that the chemical reaction makes the system stable and no convective motion can be expected for $D_a/\mathrm{R}{\mathrm{a}}^2>2.5\times {10}^{-3}$.