Place shelf liners in the drawers to reduce the amount of cedar emitting from the wood. Typically, you must cut the shelf liners to fit the drawers. Some liners you peel and stick, and others grip the surface without adhesives.
Apply a coat of shellac or polyurethane inside the drawers to seal in the cedar smell. Read the label for proper use. Air out the drawers for several days before storing your clothes to give the shellac or polyurethane smells time to dissipate.
Place a box of baking soda or a bowl of kitty litter in each drawer. These materials absorb odors and may help minimize the cedar smell.
Add another scent to the drawer to help mask the smell of cedar on your clothes. For example, you can place a sachet of potpourri, a bar of scented soap or a dryer sheet in each drawer.