We report the observation of the ${A}_{g}$-symmetric one-magnon Raman peak in the magnon Bose-Einstein condensation phase of ${\text{TlCuCl}}_{3}$. Its Raman shift traces the one-magnon energy at the magnetic $\ensuremath{\Gamma}$ point, and its intensity is proportional to the squared transverse magnetization. The appearance of the one-magnon Raman scattering originates from the exchange magnon Raman process and reflects the change of the magnetic-state symmetry. By using the bond-operator representation, we theoretically clarify the Raman selection rules, which are consistent with the experimental results.