Animating a mask is no different than animating any other layer. Any object on a mask layer may be converted into a symbol and tweened.
Open the example saved as AdvancedAnimation/demos/Mask-Animated.fla. Scrub the timeline and you will see the mask moves across the screen. Test the movie to see the final product. If the animation does not render out the way you expected, please check to make sure your layers are locked.