Ezekiel bread is best kept refrigerated or frozen unless you plan to eat the bread within 5 days.
Ezekiel bread is usually sold frozen to help preserve the bread so I always keep the bread frozen until I'm ready to use it and then place the bread in the refrigerator a day before I plan to eat the bread.
That allows enough time for the bread to thaw out and the freezer keeps the bread from going moldy.
If you plan to eat the Ezekiel bread within 4 to 5 days you can usually keep the bread out of the refrigerator and in a bread box or other dark place.
Just be sure to check the bread for mold growth as Ezekiel bread usually goes moldy sooner than other breads if not frozen or refrigerated.