Remove the drawer from the furniture and empty it out.
Lay a tarp, newspapers or an old blanket outside in a sunny spot and set the drawers on top of it with the opening facing up.
Allow the drawers to sunbathe for three to four hours so that the warm sunshine has an opportunity to dry up the mold spores.
Mix an antibacterial wood soap with water per the manufacturer's instructions.
Dip an absorbent cloth or sponge into the soapy water and wipe down the inside of the drawer thoroughly.
Wipe down the inside of the drawer with a clean, dry cloth to eliminate excess moisture.
Set the drawer back outside to air dry in the sunshine for one to two hours.
Put the drawer back in the furniture and set a dish or open box of baking soda inside to absorb any residual odor. Leave the baking soda in the drawer for at least 24 hours.