Fill a large, deep skillet with lightly salted water and bring to a rolling boil; stir in tortellini and return to a boil. Cook uncovered, stirring occasionally, until pasta floats to the top and the filling is hot, 5 to 7 minutes. Drain and set aside.

Melt butter in the same skillet over low heat. Add tomato, onion, garlic, and red pepper flakes. Cook until onion begins to brown and garlic is fragrant, about 5 minutes. Add spinach; cook, stirring constantly, until wilted, about 2 minutes. Add tortellini and prosciutto; stir until heated through. Season with salt and pepper.