It is not Necessary to Wait Until Honeydew has Reached Its Full Maturity Before Eating It.
Honey ripens after it is collected, so there is no need to worry about it ripening inside or outside of the refrigerator. When it comes to melons, including honeydew, there is less of a chance that they will ripen improperly if they are stored in the refrigerator than there is with other fruits.
You can keep honeydew for up to four days at room temperature, or you can store it in the refrigerator for up to ten days; however, you are not required to do either of these things.