In a recent breakthrough experiment, excitons in the copper oxide \(\mathrm{Cu_2O}\) have been optically excited to Rydberg states with principal quantum numbers upto \(n=25\) [Nature \(\textbf{514}\), 343 (2014)]. These fragile objects allow for the study of the quantum optical properties of light-matter interactions in semiconductors. Here we show that the details of the absorption spectrum of excitons with large \(n\) can only be understood by including coherent excitation dynamics. The measured absorption spectrum includes both the probability for absorbing a laser photon as well as a contribution relating to the coherent and incoherent parts of the intensity spectrum of the excitons. Due to the scaling of the dipole coupling of Rydberg excitons to the light field, the incoherent spectrum becomes increasingly relevant, thereby altering the shape of the absorption spectrum. In particular, additional resonances appear between the exciton peaks, which vanish if the laser pumping is substituted for white-light excitation.