Brush off any visible mildew stains with a toothbrush. Do this outside if possible so that you aren't spreading mold spores into the air.
Soak the face cloth in undiluted white vinegar for 20 to 30 minutes.
Launder the face cloth as usual, on the hottest setting that is safe for the fabric. Add chlorine bleach to the wash if the face cloth is white. If the cloth isn't white, use color safe bleach.
Dry the face cloth completely before storing it. You can do this in the dryer, or you can hang it in a sunny, well-ventilated area outdoors.