The wave packet approach to neutrino oscillation resolves contradictions that arise in the standard plane-wave approximation. It also predicts a number of potentially observable effects. This paper discusses the first experimental limits on decoherence effects based on the data of the Daya Bay experiment. The analysis of data collected in 621 days yields an upper limit on the relative wave packet momentum dispersion of $\sigma_{rel} < 0.20$ at $95\%$ C.L. Furthermore, the effect due to the wave packet nature of neutrino oscillation is found to be insignificant for the Daya Bay experiment, which ensures an unbiased measurement of the oscillation parameters $\sin^2 2\theta_{13}$ and $\Delta m^2_{32}$ within the plane wave model.