The aza-Michael polyaddition of L-arginine and N,N′-methylene-bis-acrylamide gives the biocompatible and easily cell-internalized polyamidoamine ARGO7. By controlled synthesis, two ARGO7 oligomers, namely a trimer and a pentamer, bearing acrylamide terminal units, were obtained as precursors of the β-cyclodextrin-end-terminated oligomers P3 and P5, which have been shown to encapsulate curcumin at both pH 7.4 and 4.5. After lyophilization, P3- and P5-curcumin complexes gave stable water solutions. The apparent solubility of encapsulated curcumin was in the range 20–51 μg mL−1, that is, three orders of magnitude higher than the water solubility of free curcumin (0.011 μg mL−1). The drug release profiles showed induction periods both at pH levels 4.5 and 7.4, suggesting a diffusive release mechanism, as confirmed by kinetic studies. The release rate of curcumin was higher at pH 7.4 than at pH 4.5 and, in both cases, it was higher for the P5 complex. Encapsulated curcumin was more photostable than the free drug. Molecular mechanics and molecular dynamics simulations explain at atomistic level the formation of aggregates due to favorable van der Waals interactions. The drug molecules interact with the external surface of carriers or form inclusion complexes with the β-cyclodextrin cavities. The aggregate stability is higher at pH 4.5.