I can't tell from the photo what the door is made of. Depending upon the material, you might be able to use a basic water/bleach mixture. Just make sure you don't leave the bleach on so long that it discolors the door. I would probably start with a 10-1 water-bleach ratio.
I hate mold and I'm allergic to it. Dehumidifying the room is supposed to help, and sunlight is supposed to kill mold, if you can expose it for prolonged periods.