A search for resonancelike structures in the B_{s}^{0}π^{±} invariant mass spectrum is performed using proton-proton collision data collected by the CMS experiment at the LHC at sqrt[s]=8 TeV, corresponding to an integrated luminosity of 19.7 fb^{-1}. The B_{s}^{0} mesons are reconstructed in the decay chain B_{s}^{0}→J/ψϕ, with J/ψ→μ^{+}μ^{-} and ϕ→K^{+}K^{-}. The B_{s}^{0}π^{±} invariant mass distribution shows no statistically significant peaks for different selection requirements on the reconstructed B_{s}^{0} and π^{±} candidates. Upper limits are set on the relative production rates of the X(5568) and B_{s}^{0} states times the branching fraction of the decay X(5568)^{±}→B_{s}^{0}π^{±}. In addition, upper limits are obtained as a function of the mass and the natural width of possible exotic states decaying into B_{s}^{0}π^{±}.