Energy harvesting is a promise to harvest unwanted vibrations from a host structure. Similarly, a dynamic vibration absorber is proved to be a very simple and effective vibration suppression device, with many practical implementations in civil and mechanical engineering. This paper analyzes the prospect of using a vibration absorber for possible energy harvesting. To achieve this goal, a vibration absorber is supplemented with a piezoelectric stack for both vibration confinement and energy harvesting. It is assumed that the original structure is sensitive to vibrations and that the absorber is the element where the vibration energy is confined, which in turn is harvested by means of a piezoelectric stack. The primary goal is to control the vibration of the host structure and the secondary goal is to harvest energy out of the dynamic vibration absorber at the same time. Approximate fixed-point theory is used to find a closed form expression for optimal frequency ratio of the vibration absorber. The changes in the optimal parameters of the vibration absorber due to the addition of the energy harvesting electrical circuit are derived. It is shown that with a proper choice of harvester parameters a broadband energy harvesting can be obtained combined with vibration reduction in the primary structure.