Using pp collision data corresponding to an integrated luminosity of 5.4 fb^{-1} collected with the LHCb detector at a center-of-mass energy of 13 TeV, the B^{0}→D^{-}D^{+}K^{+}π^{-} decay is studied. A new excited D_{s}^{+} meson is observed decaying into the D^{+}K^{+}π^{-} final state with large statistical significance. The pole mass and width, and the spin parity of the new state are measured with an amplitude analysis to be m_{R}=2591±6±7 MeV, Γ_{R}=89±16±12 MeV, and J^{P}=0^{-}, where the first uncertainty is statistical and the second systematic. Fit fractions for all components in the amplitude analysis are also reported. The new resonance, denoted as D_{s0}(2590)^{+}, is a strong candidate to be the D_{s}(2^{1}S_{0})^{+} state, the radial excitation of the pseudoscalar ground-state D_{s}^{+} meson.