We report on a comparison between the theoretically predicted and experimentally measured spectra of the first-forbidden nonunique β-decay transition 137Xe(7/2−)→137Cs(7/2+). The experimental data were acquired by the EXO-200 experiment during a deployment of an AmBe neutron source. The ultralow background environment of EXO-200, together with dedicated source deployment and analysis procedures, allowed for collection of a pure sample of the decays, with an estimated signal to background ratio of more than 99 to 1 in the energy range from 1075 to 4175 keV. In addition to providing a rare and accurate measurement of the first-forbidden nonunique β-decay shape, this work constitutes a novel test of the calculated electron spectral shapes in the context of the reactor antineutrino anomaly and spectral bump.