We consider the modulus stabilization by the Casimir energy in the gauge-Higgs unification scenario with the warped geometry. We analyze the one-loop effective potential and evaluate the radion and the Higgs masses. We find that these masses depend nontrivially on the Wilson line phase along the extra dimension theta_H. The radion mass varies 1-30 GeV for 0.06 < sin theta_H < 0.3, while the Higgs mass is around 150-200 GeV and depend on theta_H only logarithmically. The radion couplings to the standard model particles depend on the warp factor, but are too small to detect at collider experiments in the region where the five-dimensional description is valid.