This Letter reports the first measurement of high-energy reactor antineutrinos at Daya Bay, with nearly 9000 inverse beta decay candidates in the prompt energy region of 8-12 MeV observed over 1958 days of data collection. A multivariate analysis is used to separate 2500 signal events from background statistically. The hypothesis of no reactor antineutrinos with neutrino energy above 10 MeV is rejected with a significance of 6.2 standard deviations. A 29% antineutrino flux deficit in the prompt energy region of 8-11 MeV is observed compared to a recent model prediction. We provide the unfolded antineutrino spectrum above 7 MeV as a data-based reference for other experiments. This result provides the first direct observation of the production of antineutrinos from several high-Q_{β} isotopes in commercial reactors.