Read the laundry care tag on your coat. If "dry clean only" is on the tag, take the coat to a professional for a good cleaning. This should remove the smell.
If the coat can go in the washing machine, wash it in your regular wash with its normal amount of detergent. However, add 1/2 or 1 full cup of white vinegar to the water as soon as the washer starts agitating. Follow the instructions on the coat for drying, but do not dry the coat until the odor is removed.
Store the coat with a sheet of fabric softener in the pocket. This will help to neutralize any smells on the coat and prevent the coat from making other clothing in the closet smell as well.