We present the first measurement of dihadron angular correlations in electron-nucleus scattering. The data were taken with the CLAS detector and a 5.0 GeV electron beam incident on deuterium, carbon, iron, and lead targets. Relative to deuterium, the nuclear yields of charged-pion pairs show a strong suppression for azimuthally opposite pairs, no suppression for azimuthally nearby pairs, and an enhancement of pairs with large invariant mass. These effects grow with increased nuclear size. The data are qualitatively described by the gibuu model, which suggests that hadrons form near the nuclear surface and undergo multiple scattering in nuclei.These results show that angular correlation studies can open a new way to elucidate how hadrons form and interact inside nuclei.