With the advantages of scalability and high reliability, the distributed automated guided vehicle (AGV) system has become a significant development trend for building intelligent manufacturing workshops and achieving intelligent logistics in the workshops. The work aims to clarify the distributed AGV task allocation (DAGVTA) in intelligent manufacturing workshops, as a fundamental key issue, that affects resource utilization and production costs. Correspondingly, deep reinforcement learning was introduced, each AGV was regarded as an independent agent, and a multi-agent reinforcement learning method independent deep Q-network (IDQN) was utilized for solution. Firstly, the DAGVTA problem was transformed into a partially observable Markov decision process related to reinforcement learning. The workshop environment states observed by each AGV were used as inputs to the neural network, and the neural network was fitted with a value function to output the action selection for each AGV. Meanwhile, the reward function was designed with the transport distance of material handling tasks as the optimization objective. Furthermore, various agents were trained on the IDQN architecture, in which each agent in the environment was independent, and took actions based on local observation information. Finally, the experimental study in scenarios with different problem scales was conducted to verify the feasibility of the proposed model and method by comparing their solution effects with rule-based task allocation algorithms and the market-based bidding algorithm. After training, the AGV agent has a certain degree of autonomous collaboration ability and can collaborate to complete all transportation tasks without a centralized planner.