The ground state electronic structure of oxidized azurin from Pseudomonas aeruginosa and its optical response have been investigated by combining hybrid quantum mechanics/molecular mechanics simulations with time-dependent density functional theory. In agreement with experiment, we find that the unpaired electron spin density is mainly localized on the copper ion. The vertical absorption spectrum in the visible range is well reproduced, with the central band centered around 2.1 eV. The anisotropic dipolar field due to the extended alpha-helix polarizes the metal binding site and is responsible for a shift of the absorption bands by +/- 0.1-0.2 eV. At 300 K, the bond distances of the copper binding site undergo large fluctuations (similar to 0.3 A). It is crucial to take these thermal fluctuations into account for a faithful description of the optical properties.