An angular analysis of B^{0}→J/ψK^{+}π^{-} decays is performed, using proton-proton collision data corresponding to an integrated luminosity of 3 fb^{-1} collected with the LHCb detector. The m(K^{+}π^{-}) spectrum is divided into fine bins. In each m(K^{+}π^{-}) bin, the hypothesis that the three-dimensional angular distribution can be described by structures induced only by K^{*} resonances is examined, making minimal assumptions about the K^{+}π^{-} system. The data reject the K^{*}-only hypothesis with a large significance, implying the observation of exotic contributions in a model-independent fashion. Inspection of the m(J/ψπ^{-}) vs m(K^{+}π^{-}) plane suggests structures near m(J/ψπ^{-})=4200 and 4600 MeV.