It depends on your standards and what you mean by sourdough and bread. Lunds/Byerlys bakery would have something labeled as such, but it's a very poor example. Probably whatever you could find at Super Target likewise.
The closest possibility I can think of would be Chez Arnaud in Maple Grove or Plymouth. Most of their breads are not naturally leavened, but IIRC they do a few varieties. Their baking schedule and availability varies by day.
The only real (and good) artisan sourdoughs I have had here are Patisserie 46 and Rustica. Both in Mpls.