A search for the exotic meson X(5568) decaying into the Bs0π± final state is performed using data corresponding to 9.6 fb−1 from pp¯ collisions at 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 Bs0 produced through the X(5568)→Bs0π± process.