This article deals with the analysis and design of an active spatial mechanical vibration absorber and verification of its performance in collocated and non-collocated vibration absorption of a spatial flexible primary structure. The considered active absorber with six degrees of freedom has six identical natural frequencies. It is a so-called unifrequency absorber. The unifrequency property is achieved by delayed feedback, according to the concept of a delayed resonator. A proper tuning of the delayed feedback compensates the damping and variations in stiffness of mechanical parts, resulting in the behavior of an ideal absorber. The absorber was attached to a three-dimensional flexible frame with many degrees of freedom transformed to a reduced order model in modal coordinates. The use of a unifrequency absorber for two types of tasks is shown in this article. In the collocated case, the absorber is placed at the location where we want to suppress vibration. Such a placement is often not possible for various reasons. Therefore, the non-collocated absorber is also investigated which is remote from the point of desired vibration suppression. The absorber has considerable potential for use in improving the dynamic behavior of robots, complex rotor systems, and other mechanical systems suffering from unwanted fully spatial vibrations.