A blog on the Sharpie website recommends removing permanent marker stains by rubbing baby oil on the skin, followed by washing the area with soapy water. The oil has the capacity to break down the marker.
Another way to remove permanent marker from skin is to use a cotton ball or paper towel partially soaked with rubbing alcohol to scrub the colored area of skin, followed by soap and water. Gritty hand soaps may also be effective in removing marker stains. Milk or facial cleansers are also known to help remove these types of stains when applied with a cotton ball or paper towel. Anything mildly acidic, such as vinegar or hot sauce, can also work on permanent marker stains.
It is easiest to remove the stain when it first happens, to prevent the stain from being absorbed too deeply into the skin. Permanent marker is not intended for use on skin; though it is not toxic, it shouldn't be used to intentionally draw on any portions of the human body. Nonetheless, even without washing, the marker stain typically comes off in several days. The top layer of human skin naturally sloughs off in that amount of time, taking the stain with it. However, the stain may stay longer if the skin is especially dry.