Step 2. Wrap the Brussels sprouts in a plastic bag and place them in the crisper of your refrigerator. Do not wash them first. Brussels sprouts will keep for about five to ten days in normal refrigerator temperatures.However, if you can store Brussels sprouts like the professionals can--in 32 degrees F with a relative humidity of 95 to 100%--then they will store for up to five weeks.reeze Brussels sprouts by first washing and then cooking them in boiling water for three to five minutes. Drain, cool and package in a freezer bag. Be sure as much air is removed as possible before sealing the bag. Store for up to a year.