The picking manipulators, as the core component of fresh fruit picking robots, are responsible for complex tasks such as approaching, grasping, and transferring fruits. The development of specialized picking arms is a critical research focus in this area. However, position errors of manipulators are increased by manufacturing tolerances, assembly errors, and joint flexibility. Existing research has concentrated predominantly on error calibration for manipulators with rotational joint configurations, while less attention has been devoted to the systematic and dynamic error calibration of specialized manipulators, such as long-stroke hybrid picking arm. An error calibration method for fruit picking manipulators was proposed by utilizing machine learning techniques to enhance motion accuracy. Firstly, an error model of the picking manipulator was formulated based on its geometric configuration, establishing the relationship between system parameters and terminal pose errors. Redundant parameters were subsequently eliminated via orthogonal triangle decomposition. To minimize the influence of system errors on motion accuracy, system parameters were identified by using the least squares method, while dynamic errors were predicted via a back propagation neural network. Finally, systematic and dynamic error compensations were implemented through an inverse kinematics error compensation framework. Simulation results indicated the average error identification accuracy of this method was 89.985%, and determinant coefficient R2 was 0.950. Physical experiment demonstrated that, after compensation, the average position error and root mean square error were reduced to 0.486 mm and 0.395 mm, respectively, while the average attitude error and root mean square error were reduced to 0.395° and 0.328°, respectively. The proposed method thus significantly enhanced the motion accuracy of picking manipulators.