Oil and gas pipeline networks require the periodic inspection of their infrastructure, which can cause gas and oil leakage with several damages to the environment and human health. For this, non-destructive testing (NDT) techniques of low-cost and easy implementation are required. An option is the metal magnetic memory (MMM) method, which could be used for real-time monitoring defects of ferromagnetic structures based on the analysis of self-magnetic leakage fields distribution around each defect. This method only requires magnetic sensors with high resolution and a data processing system. We present a measurement system of tangential and normal MMM signals of three rectangular defects of an ASTM A-36 steel pipe. This system is formed by a magnetoresistive sensor, an Arduino nano and a virtual instrumentation. The measured magnetic signals have non-uniform distributions around the rectangular defects, which have small differences with respect to the results obtained of a 2D magnetic dipole model. The size of each rectangular defect is related to the amplitude and shape of its tangential and normal MMM signals. The proposed system could be used for real-time monitoring of the size and location of rectangular defects of ferromagnetic pipes. This system does not require expensive equipment, operators with high skill level or a special treatment of the ferromagnetic samples.