The interaction between a penetrating-type circular-arc crack and a screw dislocation in magnetoelectric composites is studied. Firstly, according to the basic equations of magnetoelastic composites and the theory of complex function, the relationship between the anti-plane shear stress, the normal component of the electric displacement, and the normal component of the magnetic induction along the boundary arc c is derived. Then, based on the conformal mapping technique, the complex form of the generalized stress field is obtained by analyzing the stress conditions of the dislocation. In order to discuss the dislocation, dislocation shielding effect, and crack shielding effect at the crack tip, the force-electric-magnetic field intensity factors and the image forces acting on the dislocation are further deduced. By analyzing the analytical solutions and numerical examples, the results show that the shielding effect of the field strength factor decreases with increasing the distance between the circular-arc crack tip and the dislocation point, and the angle formed by their connecting line and the positive half of the x-axis, indicating that the dislocation has a shielding effect on the crack. Additionally, the effect of dislocation on a circular-arc crack is more prominent than on a straight crack. Besides, the image force on the dislocation is affected by the surface properties of the circular-arc crack. Finally, the screw dislocation can reduce the stress intensity factor of the circular-arc crack tip, and the shielding effect rapidly weakens as the angle increases. The shielding effect of the screw dislocation on the crack tip is strengthened as the ratio between the distance from the dislocation point to the crack tip and the half-chord length of the circular-arc crack increases. These conclusions carry meaningful significance for fracture mechanics research and provide a theoretical basis for improving and evaluating the performance of electromagnetic devices.