Inertial Measurement Units (IMUs) have become a widely used tool for rehabilitation and other application domains in which human motion is analyzed using an ambulatory or wearable setup. Since the magnetic field is inhomogeneous in indoor environments and in the proximity of ferromagnetic material, standard orientation estimation and joint angle calculation algorithms often lead to inaccurate or even completely wrong results. One approach to circumvent this is to exploit the kinematic constraint that is induced by mechanical hinge joints and also by approximate hinge joints such as the knee joint and the finger (interphalangeal) joints of the human body. We propose a quaternion-based method for joint angle measurement for approximate hinge joints moving through inhomogeneous magnetic fields. The method exploits the kinematic constraint to compensate the error that the magnetic disturbances induce in the IMU orientation estimates. This is achieved by realtime estimation and correction of the relative heading (azimuth) error that is caused by the disturbance. Since the kinematic constraint does not allow heading correction when the joint axis is vertical, we extend the proposed method such that it improves accuracy and robustness when the joint is close to that singularity. We evaluate the method by simulations of a quick hand motion and study the effect of inaccurate sensor-to-segment (anatomical) calibration and joint constraint relaxations. As a main result, the proposed method is found to reduce the root-mean-square error of the joint angle from 25.8° to 2.6° in the presence of large magnetic disturbances.