Intentional breaking of the lattice symmetry in solids is a key concept to alter the properties of materials by modifying their electronic band structure. However, the correlation of strain-induced effects and breaking of the lattice symmetry is often indirect, resorting to vibrational spectroscopic techniques, such as Raman scattering. Here, we demonstrate that reflectance anisotropy spectroscopy (RAS), which directly depends on the complex dielectric function, enables the direct observation of electronic band structure modulation. Studying the strain-induced symmetry breaking in copper, we show how uniaxial strain lifts the degeneracy of states in the proximity of the both L and X symmetry points, thus altering the matrix element for interband optical transitions, directly observable in RAS. We corroborate our experimental results by analyzing the strain-induced changes in the electronic structure based on ab initio density functional theory calculations. The versatility to study breaking of the lattice symmetry by simple reflectance measurements opens up the possibility to gain a direct insight on the band structure of other strain-engineered materials, such as graphene and two-dimensional transition metal dichalcogenides.