When selecting, choose those that are heavy feeling with stems that firmly attached. When storing, place the Calabaza squash in a cool dry area if it has not been sliced open. Whole Calabaza squash can be stored for a month or a little longer while cut Calabaza should be refrigerated in an airtight container or bag and used within a week or 10 days. This type of squash also can be frozen for up to a year in airtight containers.