The recent reported 750 GeV diphoton excess at the 13 TeV LHC is explained in the framework of effective field theory assuming the diphoton resonance is a scalar (pseudoscalar) particle. It is found that the large production rate and the broad width of this resonance are hard to be simultaneously explained if only visible final states are considered. Therefore an invisible decay channel to dark matter (DM) is strongly favored by the diphoton resonance with a broad width, given a large coupling of the new scalar to DM. We set constraints on the parameter space in this scenario using the results from LHC Run 1, DM relic density, and DM direct and indirect detection experiments. We find that the DM searches can exclude a large portion of the parameter regions accounting for the diphoton excess with a broad width. (C) 2016 The Authors. Published by Elsevier B.V.