Heat olive oil in a large skillet over medium-high heat.
Add the cubed chicken to the skillet and cook until browned on all sides, approximately 5-7 minutes.
Stir in the minced garlic, oregano, salt, and pepper; cook for 1-2 minutes until fragrant.
Reduce heat to low and sprinkle mozzarella cheese evenly over the chicken. Cover with a lid for 1-2 minutes until the cheese is melted.
Spread a tablespoon of mayonnaise on each low-carb tortilla.
Layer fresh spinach onto the tortillas, then divide the cheesy garlic chicken mixture evenly among them.
Roll the tortillas tightly to form wraps and serve immediately.