Self-assembly of molecular systems is an important and general problem that intertwines physicschemistry, biology, and material sciences. Through understanding of the physical principles of self-organization it often becomes feasible to control the process and to obtain complex structures with tailored properties, for example bacteria colonies of cells or nanodevices with desired properties. Theoretical studies and simulations provide an important tool for unraveling the principles of self-organization and, therefore, have recently gained an increasing interest. The present article features an extension of a popular code MBN EXPLORER (MesoBioNano Explorer) aiming to provide a universal approach to study self-assembly phenomena in biology and nanoscience. In particular, this extension involves a highly parallelized module of MBN EXPLORER that allows simulating stochastic processes using the kinetic Monte Carlo approach in a three-dimensional space. We describe the computational side of the developed code, discuss its efficiency and apply it for studying an exemplary system.