Inclusion complexes (ICs) composed of α-cyclodextrin (α-CD) and poly(d,l-lactic acid) (PDLLA), with 10/24 (IC1) and 15/46 (IC2) (% w/w) of PDLLA incorporated/initial PDLLA weight percentage, were prepared and characterized mainly by dielectric relaxation spectroscopy (DRS). Bulk PDLLA was also analyzed for comparison. DRS was revealed to be a suitable tool to distinguish the dynamical response of the PDLLA regions constrained in between α-CD channels from the fraction incorporated inside channels. While the cooperative α-process undergoes a dramatic depletion shifting to higher temperatures (∼4.5 °C) for the PDLLA interchannels portion, it is suppressed for PDLLA chains inside pores. It was demonstrated that the broad secondary relaxation of bulk PDLLA is the Johari-Goldstein process (βJG-process). The detection of its analogue in the ICs at higher frequencies, to a greater extent in IC1, is interpreted as a true confinement effect where the dimensions of the α-CD channels interfere with the length scale of the βJG-process. The limit predicted in the framework of the coupling model, where the α-relaxation transforms in the βJG-process, seems to be reached in the ICs. Furthermore, it was found that the length scale of the additional γ process only detected in the ICs is inferior to inter- or intrachannel dimensions.