Bring a large pot of salted water to a boil. Add whole wheat fettuccine and cook according to package instructions until al dente, about 10-12 minutes. Drain and set aside.
While the pasta cooks, heat olive oil in a large skillet over medium heat.
Season chicken breasts with salt and pepper on both sides.
Add chicken breasts to the skillet and cook for 6-7 minutes on each side or until cooked through and internal temperature reaches 165°F (74°C). Remove from skillet and let rest for 5 minutes, then slice into strips.
In the same skillet, add minced garlic and sauté for 1 minute until fragrant, stirring constantly to avoid burning.
Sprinkle flour over the garlic and stir to combine, cooking for 1 minute to remove raw flour taste.
Gradually whisk in low-fat milk, stirring constantly to avoid lumps. Cook for 3-4 minutes until sauce thickens slightly.
Remove skillet from heat and whisk in Greek yogurt, Parmesan cheese, ground nutmeg, salt, and pepper until smooth and creamy.
Add cooked pasta and sliced chicken back into the skillet. Toss gently to coat evenly with the Alfredo sauce.
Sprinkle chopped fresh parsley over the top and serve immediately.