A search for the exotic meson X(5568) decaying into the B_{s}^{0}π^{±} final state is performed using data corresponding to 9.6 fb^{-1} from pp[over ¯] collisions at sqrt[s]=1960 GeV recorded by the Collider Detector at Fermilab. No evidence for this state is found and an upper limit of 6.7% at the 95% confidence level is set on the fraction of B_{s}^{0} produced through the X(5568)→B_{s}^{0}π^{±} process.