Preheat the oven to 450 degrees Fahrenheit. Place a wire rack on a foil-lined baking sheet, and set it aside.
Put the flour in a shallow dish. Put the panko in another shallow dish. In a medium bowl, whip the egg whites with a whisk until they are extremely foamy but not quite holding peaks.
Working in batches, dredge the mozzarella sticks in the flour, shaking off any excess. Add the mozzarella sticks to the egg whites and toss to coat completely. Add the mozzarella sticks, a few pieces at a time, to the panko and coat completely.