We study the Vainshtein mechanism in the context of slowly rotating stars in scalar-tensor theories. While the Vainshtein screening is well established for spherically symmetric spacetimes, we introduce a slow rotation of the source and examine its validity in the axi-symmetric case. We solve for the frame-dragging function accounting for the slow rotation and show that the deviations from the general relativity (GR) solution are screened in the weak-field approximation, meaning the solution for the frame-dragging function is the same as GR to leading order. This suggests that the Vainsh