Read the label on the shirt before you do anything else. The care instructions will tell you what is safe and what is not safe for the fabric.
Hand-wash delicate items in warm water and mild detergent. Sweaters, for example, are sometimes better hand washed than put in the washing machine, which can damage the delicate fibers and cause the sleeves to shrink.
Take the shirt to the dry cleaners if the label says "dry clean only." Not following this direction could result in a shrunken shirt.
Keep your shirt out of the dryer. Hang it on a hanger to dry or lay it flat. The heat from the dryer can easily cause the fabric, including the sleeves, to shrink.