Weak magnetic detection technology is an effective method to identify stress-induced damage to ferromagnetic materials, and it especially possesses great application potential in long-distance oil and gas pipeline weld crack detection. In the process of pipeline operation, due to internal pressure and external loads, local stress concentration may be generated, and partial stress concentration may lead to local cracks and expansion of the pipe. In order to improve the accuracy of magnetic signal analysis for ferromagnetic materials under internal pressure, the causes of magnetic signal generation at pipeline welds were analyzed from a microscopic perspective. The distributions of magnetic signals at pipeline welds, weld cracks, and base metal cracks under different internal pressures were numerically analyzed. The variation trends of magnetic signal characteristics, such as peak values of axial and radial components, gradient K, maximum gradient Kmax, and gradient energy factor S(K), were analyzed. In addition, experiments were carried out to verify the numerical data. It was revealed that with the elevation of internal pressure, the peak values of the axial and radial components, gradient K, maximum gradient Kmax, and gradient energy factor S(K) linearly increased. However, the magnitude and average change of S(K) were larger, which can more directly indicate variations of magnetic signals. The radial growth rate νy of S(K) was 3.24% higher than the axial growth rate νx, demonstrating that the radial component of the magnetic signal was more sensitive to variations of stress. This study provided a theoretical and experimental basis for detection of stress-induced damage to long-distance oil and gas pipelines.