Recent high-resolution absorption spectroscopy on excited excitons in cuprous oxide [Nature (London) 514, 343 (2014)NATUAS0028-083610.1038/nature13832] has revealed significant deviations of their spectrum from that of the ideal hydrogen-like series. Here we show that the complex band dispersion of the crystal, which determines the kinetic energy of electrons and holes, strongly affects the exciton binding energy. Specifically, we show that the nonparabolicity of the band dispersion is the main cause of the deviation from the hydrogen series. Experimental data collected from high-resolution absorption spectroscopy in electric fields validate the assignment of the deviation to the nonparabolicity of the band dispersion.