For the low carbon distributed assembly permutation flow-shop scheduling problem(LC_DAPFSP), a mathematical model with the goal of minimizing the total energy consumption and the makespan is established, and then a multidimensional estimation of distribution algorithm(MEDA) is proposed to solve this problem. Firstly, a population is initialized by utilizing a random method and a heuristic algorithm. Secondly, a matrix-cube-based probabilistic model is developed to reasonably learn and accumulate the information of the job blocks and the jobs' order from the superior solutions, and an effective sampling mechanism is designed to sample the probability model to generate new population, so as to reasonably guide the searching directions and find the promising regions in the solution space. Then, to balance the exploration and the exploitation capabilities of the algorithm, a problem-dependent variable neighborhood search method is developed to perform an in-depth exploitation in the promising regions found by the global search. Finally, simulations and comparisons demonstrate that the proposed MEDA can effectively solve the LC_DAPFSP.