The knowledge of prompt fission $\ensuremath{\gamma}$-ray emission has been of major interest in reactor physics for a few years. Only few experimental spectra were published until now for fast-neutron-induced fission, and measurements would be also valuable in order to improve our understanding of the fission process. A simple experimental method was used to measure the first prompt fission $\ensuremath{\gamma}$-ray spectra up to 10 MeV. In this approach, the $\ensuremath{\gamma}$ rays are measured with a bismuth germanate (BGO) detector which offers two significant advantages with respect to other $\ensuremath{\gamma}$-ray detectors: a high peak-to-total ratio and a high efficiency. The prompt fission neutrons are rejected by the time-of-flight technique between the BGO detector and a fission trigger given by a fission chamber. Prompt fission $\ensuremath{\gamma}$-ray spectra were measured for 1.6 \ifmmode\pm\else\textpm\fi{} 0.1, 5.1 \ifmmode\pm\else\textpm\fi{} 0.2 and 15.0 \ifmmode\pm\else\textpm\fi{} 0.6 MeV neutron-induced fission on $^{238}\mathrm{U}$ at the CEA, DAM, DIF Van de Graaff accelerator; average multiplicity and mean photon energy per fission were deduced from the spectra.