If your fresh Mozzarella doesn't come in a tub of liquid, store it in the refrigerator in fresh water and use within 2 to 3 days at the most. The best way to keep mozzarella fresh is to store it in the refrigerator in a container of cold water.Change the water daily. Store in mozzarella cheese in the refrigerator at a temperature between 34 degrees F. and 40 degrees F. Remove from the refrigerator at least 1 hour before you plan to serve it.Freezing is not recommended.hange the water daily. Store in mozzarella cheese in the refrigerator at a temperature between 34 degrees F. and 40 degrees F. Remove from the refrigerator at least 1 hour before you plan to serve it. Freezing is not recommended.