Anthocyanins are the main active compounds in blueberry. However, they have poor oxidation stability. If anthocyanins are encapsulated in protein nanoparticles, their oxidation resistance could be increased as a result of the slowing down of the oxidation process. This work describes the advantages of using a γ-irradiated bovine serum albumin nanoparticle bound to anthocyanins. The interaction was characterized biophysically, mainly by rheology. By computational calculation and simulation based on model nanoparticles, we estimated the number of molecules forming the albumin nanoparticles, which allowed us to infer the ratio of anthocyanin/nanoparticles. Measurements by UV-vis spectroscopy, FTIR spectroscopy, fluorescence spectroscopy, dynamic light scattering (DLS), ζ potential, electron transmission microscopy, and rheology at room (25 °C) and physiological (37 °C) temperatures were performed. The spectroscopy measurements allowed identifying additional hydrophobic sites created during the irradiation process of the nanoparticle. On the basis of the rheological studies, it was observed that the BSA-NP trend is a Newtonian flow behavior type for all the temperatures selected, and there is a direct correlation between dynamic viscosity and temperature values. Furthermore, when anthocyanins are added, the system increases its resistance to the flow as reflected in the morphological changes observed by TEM, thus confirming the relationship between viscosity values and aggregate formation.