Rayon fabric does shrink in the dryer. Some rayon clothing is labeled as washable, which means it can be machine washed, but it should still be hung or laid flat to dry.
If clothing is labeled "dry clean only," it should never be washed in the washer or dried in a clothes dryer. Doing so could damage the fabric or shrink it considerably. According to Fabric Link, rayon is a comfortable fabric that dyes well, but it is weakest when it is wet and shrinks if not cared for properly. It is important to read the label for washing instructions to extend the life of rayon clothing.