Roll the collard burrito one at a time. Lay the collard leaf on a flat surface or use a wooden cutting board.
Start at the upper portion of the leaves. Fill each leaf with rice (about 1/4 cup), if using large leaves, fill with more rice. Add avocado, lettuce, tomato, and Greek yogurt.
Roll from the top, when you reach the middle, fold the two sides of the leaf and continue rolling. Secure the wrap, cut in half.