Heat margarine in a Dutch oven over medium heat until melted. Add potato, onion, and celery to Dutch oven; cook, stirring constantly, 5 minutes. Add broth and next 4 ingredients; bring to a boil. Cover, reduce heat, and simmer 15 minutes.
Remove 2 cups vegetables from broth with a slotted spoon; partially mash vegetables with a fork or potato masher. Return vegetables to Dutch oven. Add turkey and milk; bring to a boil over medium heat, stirring constantly. Combine flour and water, stirring until smooth. Gradually add flour mixture to Dutch oven; cook over medium heat, stirring constantly, 4 to 5 minutes or until thickened and bubbly.