Complex ac susceptibility, chi = chi' - i chi '', measurements of the clathrate compound Pr3Pd20Ge6 were performed in static fields up to 10 mT for H parallel to [001] and at temperatures down to 500 mu K. Praseodymium (Pr) nuclear magnetic moments at the 8c site, where quadrupole moments of 4f electrons order at T-Q1 = 250 mK, were found to order antiferromagnetically at 9 mK, as shown by a peak in chi' and a substantial increase in thermal relaxation time. The large enhancement factor (1 + K-8c) obtained by calculation of the hyperfine-enhanced nuclear susceptibility of Pr at the 8c site accounts for the high transition temperature of Pr nuclear magnetic moments and the large chi' below 30 mK. From analysis of the crystalline electric field and the mean-field approximation, we conclude that a chi peak at 77 mK can be ascribed to an antiferromagnetic ordering of magnetic moments of 4f electrons at the 4a site. We found that nuclear and f-electron moments order separately on two sublattices in this compound. The temperature and magnetic field dependence of chi' and chi '' between 30 and 60 mK are discussed in terms of dissipation phenomena.