A recent theoretical study has suggested that muons can enhance proton-boron-11 (p-${}^{11}$B) reaction cross-section by several orders of magnitude in the low-energy regime. In this work, we investigate this reaction process using a semi-classical treatment, that is, a muon and a proton first form a muonic hydrogen atom p$\mu$, which subsequently collides with a ${}^{11}$B nucleus. During the collision, the p$\mu$ atom approaches the ${}^{11}$B nucleus and is then repelled by the Coulomb repulsive potential. At the distance of closest approach between the proton and the ${}^{11}$B nuclei in this classical scattering process—namely, the classical turning point—quantum tunneling through the Coulomb barrier can occur, allowing the proton to penetrate into the range of the nuclear force of the ${}^{11}$B and trigger the fusion reaction. We determine the turning point statistically by using the classical trajectory Monte Carlo method, where the initial phase-space distributions of the proton and muon are sampled from the ground-state microcanonical distribution. Our results show that, compared with the bare-nucleus case, the reaction cross-section is enhanced by several orders of magnitude in the low-energy region. A comparison with the static charge-shielding treatment reveals certain differences; however, both approaches demonstrate that the catalytic effect of the muon can significantly enhance the low-energy p-${}^{11}$B reaction cross-section.