Heat the olive oil in a skillet over medium-high heat; cook and stir the onion in the hot oil until fragrant, about 3 minutes. Add the squash in three batches, making sure the first has softened slightly before adding the next. Season with salt.
Heat the tortillas in the microwave until warm, about 10 seconds. Spoon the squash mixture into the center of the tortillas; top with the Cheddar cheese and tomato. Roll into a burrito to serve.