The influence that dipole-dipole interactions exert on the dynamics of the magnetization of nanometer-sized Co clusters has been studied by means of ac and dc susceptibility experiments. These clusters grow in a quasiordered layered structure, where all relevant parameters can be tailored and measured independently. Our data show without ambiguity that the magnetic relaxation becomes slower as the degree of interaction increases. The effective activation energy increases linearly with the number of nearest neighbor clusters, evolving from the value for a 2D layer to the fully 3D behavior, which is nearly reached for five layers. The experimental results agree quantitatively with the predictions of a simple model.