Complex multiphase flow in oil and gas pipelines raises safety risks. Magnetic flux leakage (MFL) detection effectively identifies pipeline defects. However, the high-speed movement of MFL inspection tools induces motion-induced eddy currents (MIECs), complicating defect recognition and quantification. Most prior research has primarily focused on rectangular defects, leaving a gap in understanding the impact of MIECs on weld defects. This paper proposes the amplitude and shape deformation coefficients to analyze the influence of velocity on various weld defects, including internal reinforcement, lack of penetration, crack, external corrosion, internal corrosion, porosity, and lack of fusion. Utilizing these coefficients, this study examines the influence of the defect size and magnetizer configuration on these velocity-induced effects. The results show that the shape deformation coefficients range from 2.75 to 3.57 for Bx and from −0.13 to −0.3 for By, indicating a significant change in the MFL signal shape at 10 m/s compared to 0 m/s. The amplitude deformation coefficients for lack of penetration, internal corrosion, and porosity range from −0.01 to 0.1 for Bx, and from 0.86 to 0.98 for By, suggesting a decrease in peak-to-peak values. In contrast, other defects exhibit an increase in peak-to-peak values, indicating that the velocity effect may enhance the MFL signal. Also, the defect size and magnetizer configuration can affect the velocity effect on signals. These findings provide essential guidance for quantifying defect sizes and a solid foundation for designing more effective magnetization devices.