We have determined the effects of the electron-phonon and hole-phonon interactions on the binding energies of excitons in cylindrical quantum wires in the presence of an external electric field. The exciton binding energies of several Ⅲ-Ⅴ and Ⅱ-Ⅵ compound semiconductor quantum wire structures have been calculated as functions of the electric fields and the transverse dimension of the quantum wires. Theoretical results show that the exciton-phonon coupling reduces both the exciton binding energies and the Stark shifts by screening the Coulomb interaction; thus, the exciton-phonon coupling is significant and cannot be neglected.