In a mixing bowl, combine shredded chicken, Greek yogurt, garlic powder, smoked paprika, and black pepper until evenly coated.
Lay tortillas flat and divide the chicken mixture onto the center of each.
Top the chicken with shredded mozzarella cheese.
Fold the left and right edges of the tortilla toward the center, then roll tightly from the bottom to form a sealed wrap.
Preheat air fryer to 375°F (190°C).
Lightly spray the wraps with olive oil and place them seam-side down in the air fryer basket.
Air fry for 8 minutes, flipping halfway through, until the exterior is golden and crisp.
Allow to rest for 2 minutes before serving.