The T2K Collaboration presents the first measurement of electron neutrino-induced charged-current pion production on a predominantly carbon target in a restricted kinematical phase space. This is performed using data from the 2.5° off-axis near detector, ND280. The differential cross sections with respect to the outgoing electron and pion kinematics, in addition to the total flux-integrated cross section, are obtained. Comparisons between the measured and predicted cross-section results using the neut, genie, and nuwro Monte Carlo event generators are presented. The measured total flux-integrated cross section is [2.52±0.52(stat)±0.30(syst)]×10^{-39}  cm^{2} nucleon^{-1}, which is lower than the event generator predictions.