Switzerland's two dominant supermarket chains, Coop and Migros, both carry a reasonable everyday range of dog and cat food, treats and basic supplies, and are the most convenient option for a quick restock wherever you're staying.
For a specific brand, a prescription diet, or more specialised gear, Qualipet and Fressnapf are Switzerland's main dedicated pet-store chains, with locations in most larger towns and cities.
As with everything else in this category, prices run higher than in Italy or much of southern Europe — if your pet has a specific dietary need, it's often more economical to bring a supply than to buy the full amount locally.