Swarm intelligence algorithms are designed to mimic the natural behaviors of living organisms. The birds, animals and insects exhibit extraordinary problem solving behaviors and intelligence when living in colonies or groups. These unique behaviors form the basis for the design of the Metaheuristic which are helpful in solving several real-life combinatorial optimization problems. Monkey algorithm is developed based on the unique behaviors of monkeys such as mountain and tree climbing, jumping, watching and somersaulting. This paper reports for the first time the design and development of Multi-objective Monkey Algorithm (MoMA) and its use for the design of molecules with optimal drug-like properties. Finally, the performance of the proposed MoMA for Drug design (MoMADrug) is compared with the previously disclosed Multi-objective Genetic algorithm (MoGADdrug) for the design of drug-like molecules.