Dynamic vibration absorber (DVA) is a practical tool used for sound and vibration suppression in the specific frequency band. The parameters of DVAs should be optimally tuned to obtain the best sound and vibration suppression application effects. When the DVAs are used for structural vibration reduction, DVAs’ two parameters which are the optimal frequency ratio and damping ratio have simple analytical expressions. However, the concise analytical expressions of the DVAs that are used for suppressing the structural sound radiations have not been reported. First, this paper investigates the characteristics of DVAs in suppressing sound radiation from thin plates. Second, the fixed points’ phenomenon of the sound radiations of the plate carrying DVAs is revealed. In addition, the classical fixed points’ theory is extended into the optimization process of the DVAs that are used for sound radiation control of the plate. The analytical expression of the optimal frequency ratio, as well as the damping ratio optimization method of the DVA, is simultaneously proposed. Third, the installation position of DVAs is also presented to obtain a better acoustic radiation effect. Finally, the numerical simulations are performed to verify the availability of the method. It is showed that the best sound radiation control effect could be obtained by adopting the optimization means proposed in this paper.