For safe and reliable deployment of any robot controller on the real hardware platform, it is generally a necessary practice to comprehensively assess the performance of the controller with the specific robot in a realistic simulation environment beforehand. While there exist several software solutions that can provide the core physics engine for this purpose, it is often a cumbersome and error-prone effort to interface the simulation environment with the robot controller being evaluated. The controller may have a complex structure consisting of multiple states and transitions within a finite-state machine (FSM), and may even require input through a GUI. In this work, we present mc-mujoco -- an open-source software framework that forms an interface between the MuJoCo physics simulator and the mc-rtc robot control framework. We provide implementation details and describe the process for adding support for essentially any new robot. We also demonstrate and publish a sample FSM controller for bipedal locomotion and stable grasping of a rigid object by the HRP-5P humanoid robot in MuJoCo. The code and usage instructions for mc-mujoco, the developed robot modules, and the FSM controller are available online.