The disappearance of reactor ν¯ e observed by the Daya Bay experiment is examined in the framework of a model in which the neutrino is described by a wave packet with a relative intrinsic momentum dispersion σrel. Three pairs of nuclear reactors and eight antineutrino detectors, each with good energy resolution, distributed among three experimental halls, supply a high-statistics sample of ν¯ e acquired at nine different baselines. This provides a unique platform to test the effects which arise from the wave packet treatment of neutrino oscillation. The modified survival probability formula was used to fit Daya Bay data, providing the first experimental limits: 2.38 × 10 - 17< σrel< 0.23. Treating the dimensions of the reactor cores and detectors as constraints, the limits are improved: 10 - 14≲ σrel< 0.23 , and an upper limit of σrel< 0.20 (which corresponds to σx≳10-11cm) is obtained. All limits correspond to a 95% C.L. Furthermore, the effect due to the wave packet nature of neutrino oscillation is found to be insignificant for reactor antineutrinos detected by the Daya Bay experiment thus ensuring an unbiased measurement of the oscillation parameters sin 22 θ13 and Δm322 within the plane wave model.