When dealing with complex models in real situations, many optimization problems require using more than one objective function to represent the relevant characteristics of the system under consideration adequately. This is why multiobjective optimization algorithms that can deal with several objective functions are required in order to obtain reasonable results in an adequate processing time. This paper presents the multiobjective version of a recent metaheuristic algorithm that optimizes a single objective function, known as the Majority-minority Cellular Automata Algorithm (MmCAA), inspired by cellular automata operation. The algorithm presented here will be known as the Multiobjective Majority-minority Cellular Automata Algorithm (MOMmCAA). The MOMmCAA adds repository management and multiobjective search space density control to complement the performance of the MmCAA and make it capable of optimizing multiobjective problems. To evaluate the performance of the MOMmCAA, benchmark test sets are taken (DTLZ, quadratic, and CEC-2020), along with real-world engineering design problems, compared against other multiobjective algorithms recognized for their performance (MOLAPO, GS, MOPSO, NSGA-II, and MNMA). The results obtained in this work show that MOMmCA produces comparable performance with the other metaheuristic methods, which shows it as a competitive algorithm to be used for multiobjective problems. MOMmCAA was implemented in MATLAB, and its source code can be consulted in GitHub. https://github.com/juanseck/MOMmCAA