Heat olive oil in a large skillet over medium heat. Cook and stir sweet onion in hot oil until translucent, about 5 minutes. Add turkey to the skillet in small chunks; cook and stir until the turkey is no longer pink, 5 to 7 minutes. Stir mushrooms into the turkey mixture; cook and stir until softened, 3 to 5 minutes. Season the mixture with salt and pepper.
Pour tomato sauce and diced tomatoes over the turkey mixture; add garlic and stir. Bring the mixture to a simmer and cook until the tomato sauce thickens, about 20 minutes.
Bring a large pot of lightly salted water to a boil; add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain pasta and stir into the turkey mixture; toss to coat.