In this study, dielectric constant and pyroelectric current measurements under high pressure up to 16.7 kbar have been performed for the interacting spin dimer system ${\mathrm{TlCuCl}}_{3}$, which exhibits spin-driven ferroelectricity in the magnon Bose-Einstein condensation (BEC) phase with strong quantum spin fluctuation. When pressure is applied, the magnon BEC phase becomes significantly stabilized, whereas the value of the electric polarization decreases in high-pressure regions. It is also observed that electric polarization becomes harder under pressure. Analyses based on both a Landau theory and a microscopic spin Hamiltonian demonstrate that the suppression of quantum fluctuation on the application of pressure caused the observed pressure effects. Consequently, it is revealed that the ferroelectricity in ${\mathrm{TlCuCl}}_{3}$ is highly governed by the quantum spin fluctuation.