Bring brown rice with enough water to cover in a saucepan to a boil. Reduce heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed.

Cut off red cabbage stem. Gently peel off leaves, being careful not to tear; place individual leaves into a large pot of water and bring to a boil. Cook for 5 minutes; reduce heat and simmer until tender but still crunchy and red, then drain.

Heat olive oil in a large skillet over medium-high heat. Sauté celery, onion, and garlic until softened. Mix in turkey; season with salt. Cook and stir until turkey is browned and crumbly.

Add crushed tomatoes and cooked rice to the skillet; cook, stirring occasionally, until flavors combine.

Place 1 cabbage leaf on top of each tortilla. Fill with turkey-rice mixture; fold up bottom end and roll into a tight burrito.