Kroger Co. plans to eliminate plastic shopping bags from its supermarkets, the latest retailer to address customer backlash against disposable packaging and utensils.

The largest U.S. grocery chain by stores and sales said Thursday that it would remove single-use plastic bags from its 63-store QFC chain in the Pacific Northwest next year and eliminate them from all 2,800 Kroger-owned stores by 2025.

“This...