This paper presents an indirect adaptive control method for an autonomous underwater vehicle-manipulator system (UVMS) based on an extended Kalman filter (EKF). This method overcomes the disadvantages of existing disturbance observers and direct adaptive control schemes, which are based on linear system techniques and regressor-based techniques. The proposed control scheme can be applied to UVMSs for various purposes such as payload compensation, interaction effects compensation, underwater current or external disturbance compensation, reaction compensation, and independent system control. The performance of the proposed controller was demonstrated numerically by payload compensation, where it compensated for the reaction effects experienced during a manipulation task, and disturbance (underwater current) compensation in a UVMS with a six degrees of freedom (DOF) underwater vehicle and a 3-DOF underwater manipulator.