Cu2ZnSn(S,Se)4 (CZTS(e)) solar cells suffer from low-open-circuit voltages that have been blamed on the existence of band gap fluctuations, with different possible origins. In this paper, we show from both theoretical and experimental standpoints that disorder of Cu and Zn atoms is in all probability the primary cause of these fluctuations. First, quantification of Cu-Zn disorder in CZTS thin films is presented. The results indicate that disorder is prevalent in the majority of practical samples used for solar cells. Then, ab initio calculations for different arrangements and densities of disorder-induced [CuZn+ZnCu] defect pairs are presented and it is shown that spatial variations in band gap of the order of 200meV can easily be caused by Cu-Zn disorder, which would cause large voltage losses in solar cells. Experiments using Raman spectroscopy and room temperature photoluminescence combined with in situ heat-treatments show that a shift in the energy of the dominant band-to-band recombination pathway correlates perfectly to the order-disorder transition, which clearly implicates Cu-Zn disorder as the cause of band gap fluctuations in CZTS. Our results suggest that elimination or passivation of Cu-Zn disorder could be very important for future improvements in the efficiency of CZTS(e)-based solar cells.