When it becomes too dark for your camera to properly process the image you get noise. To get ride of the noise you need to get more light to the imaging sensor. You can either open up the iris or add more light. Consumer video cameras are very poor in low light so your options are very limited. Many consumer cameras also use an "auto gain" feature when it gets too dark which adds noise as well.
Pretty much the best you can do is set the shutter speed to 1/30 of a second. It will open up the aperture and create the least grainy shot possible with the light available and the sensor you have. Otherwise. Add Light.