In a large mixing bowl, combine the shredded cooked chicken and buffalo hot sauce, tossing until the chicken is thoroughly coated.
Fold the diced celery and sliced green onions into the buffalo chicken mixture.
Lay each tortilla flat on a clean work surface.
Distribute the shredded romaine lettuce and matchstick carrots evenly across the center of the four tortillas.
Divide the buffalo chicken mixture equally among the tortillas, layering it over the vegetables.
Drizzle 1 tablespoon of dressing over the chicken in each wrap.
Roll each tortilla tightly, folding in the sides to secure the filling.
Slice each wrap in half diagonally and place into airtight meal prep containers.
Store refrigerated and serve cold with celery sticks and remaining dressing on the side.