Technically, no; a "meteor" is the glowing streak of light caused when a rock falling from space penetrates the Earth's atmosphere, and is heated to incandescence by friction and compression heating. The Moon has no atmosphere, so no atmospheric heating, so no glowing streak of light.
However, you probably meant to ask "can you see impacts on the Moon during a meteor shower on Earth?", and in that case the answer would be "Yes!". Astronomers and amateur sky watchers have been watching the Moon for impact flashes, and NASA has recorded thousands of them.